Fama-MacBeth 1973: Replication and Extension - SP …home.uchicago.edu/~serginio/research/FamaPaper_fm73... · · 2013-10-12Fama-MacBeth 1973: Replication and Extension ... alternate

Fama-MacBeth 1973: Replication and Extension

Serginio Sylvain �

Graduate School of EconomicsUniversity of Chicago

Chicago, IL 60615, USA

October 11, 2013

Abstract

I reproduce the results of Fama and MacBeth (1973) and extend this paper inseveral ways. First, I use twenty-five test portfolios constructed using a double-sort onbetas and standard deviations of the residuals of the underlying securities (while stillmaintaining the same timing assumptions and method of Fama and MacBeth; 1973).I find that the coefficient on the average standard deviation of the residuals becomessignificant in the cross-sectional regressions, even for the 1929-1968 time period. Thisgoes against some of the results in Fama and MacBeth (1973) and hints that theseresults may not have been robust. In particular, I alternate between using an equal-weighted and value-weighted NYSE portfolio as proxy for the market portfolio. I alsoalternate the construction of the test portfolio estimates between equal-weighting andvalue-weighting of the underlying securities estimates. I find that the Fama-MacBeth(1973) results are unaffected by these variations if the test portfolios are constructedusing a single sort on betas as done in Fama-MacBeth (1973). But with test portfoliosbuilt with a dual-sort much of the Fama-MacBeth (1973) results are undone.

�I am grateful to Aaron Foss for providing me with helpful comments, suggestions, and feedback.

1

1 Introduction

Fama and MacBeth (1973) proposed a method of testing some asset pricing implicationsthat arise from the assumption of normally distributed portfolio1 returns and risk-averseinvestors. In particular, these two assumption imply that investors would choose portfoliosby trading off between the expected returns and the standard deviations of returns of saidportfolios. More specifically, the investors choose portfolios that have minimum varianceper unit of expected return. Thus investors only hold portfolios that are mean-variance-efficient2 (MVE). Therefore, the expected return on any portfolio p held by investors is suchthat EpRpq � EpR0,eq � βp,erEpReq �EpR0,eqs. Here Re is the return on any MVE portfolioe, R0,e is the return on a portfolio with zero beta with respect to portfolio e, and βp,e is theregression coefficient from regressing Rp on Re.

If there exists a risk-free rate at which investors can borrow (as in the Sharpe-Lintner model)or if there is unlimited short-selling of securities (as in the Black model), with common be-liefs and efficient markets3 then the market portfolio (the value-weighted sum of all investorsportfolio holdings where the weights are given be the respective investor’s wealth) can beshown to be MVE. Thus we can replace portfolio e in the above equation with the marketportfolio M and obtain the CAPM.

Fama and MacBeth (1973) proposed the following specification to test three implicationsof this result.

Rp � γ0,t � γ1,tβp,t�1 � γ2,tβ2p,t�1 � γ3,tsp,t�1peiq � ηp,t @p (1)

The author use this specification to test

1. Linearity: EpRpq is linear in βp, the systematic risk of portfolio p. Linearity impliesthat γ2,t should not be statistically different from zero.

2. Only the systematic risk measured by βp is priced. Therefore, γ3,t should also bestatistically indistinguishable from zero.

3. There is positive expected risk-return trade-off. Thus the null hypothesis Epγ1,tq ¤ 0should be rejected.

The method used in Fama-MacBeth (1973) is very popular even today. It consists of firstusing time-series regressions of individual securities against (a proxy for) the market portfolioand then grouping the securities into twenty portfolios according to their beta coefficients.The next step is to run the cross-sectional regression using equation (1) for each month andthen calculate the average of the coefficients over the time period considered to obtain ¯γj. Iwill describe the method in detail later.

1Note that portfolios can contain one ore more securities.2For the derivation of this result, see Foundations of Finance Chap. 5, Fama (1976).3Market efficiency here means that when investors form expectations they use the “true” joint probability

density function for security prices implied by the information set that is relevant for determining securityprices (see Foundations of Finance Chap. 5, Famal; 1976)

2

Although the method is still widely used many of the results in the paper have not re-mained valid in subsequent testing periods and with further investigation. More specifically,Fama-MacBeth (1973) shows that for the time period 1929-1968 the model described abovehas performed fairly well. ¯γ2,t and ¯γ3,t were not significantly different from zero (in a statis-tical sense). Thus Fama-MacBeth (1973) fails to reject that conditional on markets beingefficient, the tests portfolios are mean-variance efficient in the set of securities spanned bythe proxy for the market portfolio and the test portfolios. However, later research wouldshow that the model performs poorly.

Indeed, in Fama and French (2006) the authors “conclude that the CAPM has fatal problemsthroughout the 1926 to 2004 period”. Furthermore, Fama and French (1996) also show thatthere may be additional state variables of interest to investors4. The authors find that athree factor model with excess returns of the market portfolio on the risk-free security, thedifference in returns between portfolios of small and large stocks and the difference in returnsbetween portfolios of high and low book-to-market value captures a lot of the anomalies inexpected returns produced by the CAPM5. With the benefit of hindsight, it is all the moresurprising that the model performed so well in the pre-1968 period. In particular, Fama andMacBeth (1973) use the equal-weighted NYSE portfolio as a proxy for the market portfo-lio. In theory, the market portfolio should be the value-weighted portfolio of total investorswealth which includes human capital and other assets not tradeable or readily measurable.Furthermore, any test of asset pricing model is a joint test of market efficiency and of theequilibrium implications of the model’s assumptions. Given the strong assumptions behindthe model, and with the benefit of hindsight it is not surprising that a fair amount of evi-dence was later found against the model.

The question I would like to address in my paper is what could have been done in Fama-MacBeth (1973) to reveal some of the flaws of the model. In particular, I replicate theauthors results and through a few robustness checks I show that the results are not consis-tent. Keeping the same method used in the paper, I alternate between using a value-weightedor equal-weighted NYSE portfolio as proxy for the market portfolio, using value-weightedor equal-weighted underlying securities estimates to build the test portfolios estimates andusing dual-sort rather than single-sort test portfolios. I find that with a double-sort on betaand standard deviation of the residuals of the underlying securities, many of the results inFama-MacBeth (1973) in favor of the model disappear.

4Or that at least additional excess returns are needed to span the true market portfolio of investor’swealth

5We should note that one cannot test the CAPM because the true market portfolio of investors’ wealth isnot observed. Furthermore, any test of the CAPM would be a joint test of the CAPM and market efficiency.Nonetheless, to be concise, to avoid confusion and to be consitent with the literature I will use CAPM todescribe the following model EpRpq � EpR0,M q � βp,M rEpRM q � EpR0,M qs; where M is a proxy for themarket porfolio (eg. NYSE value-weighted portfolio).

3

2 Method

I use the NYSE securities provided by CRSP and follow the Fama and MacBeth (1973)method. I start with a formation period of seven years during which I run the time seriesregression for each security’s monthly return, Ri,t, against the returns of the proxy for themarket portfolio (the value-weighted or equal weighted NYSE index), RM,t.

Ri,t � α � βiRM,t � ei,t

To produce the single-sort portfolios, I group the securities into twenty portfolios (one foreach beta quantile). To produce double-sort portfolios, first I sort the securities according totheir beta coefficient. Then I sort the securities in each beta-quantile according to the samplestandard deviation of the error term (spei,tq). Lastly, I group the securities into twenty-fiveportfolios (one for each of the 5 � 5 quantiles).

I follow each portfolio formation period with an estimation period where I regress the under-lying security returns of each portfolio against the returns of the market proxy. I collect thebeta coefficients and calculate the respective portfolio beta by taking an equal-weighted ora value-weighted sum of the underlying securities beta estimates. That is βp,t �

°Ni�1 xiβi,t;

where xi is the weight corresponding to security i in portfolio p. The testing period is fouryears long. In particular each month t of the testing period I run the regression specifiedby equation (1). In this cross-sectional regression βp,t is as defined above and the other

regressors6 are sp,tpei,tq �°Ni�1 xispei,tq and β2

p,t �°Ni�1 xiβ

2i,t.

The last step consists of taking the sample averages of γjt across the time periods of in-terest to obtain the desired statistics. Each estimation period is an increasing time windowwhich starts five year prior to the testing period. The estimation window increases by oneyear for every year of the testing period (excluding the first year). Thus the portfolio betasare updated annually and these betas are estimated one to twelve month prior to the dateof the portfolio returns in testing regressions. I restrict the analysis to securities that havedata for all five years of the preceding estimation period and at least four years of the for-mation period. To be consistent with Fama-Macbeth (1973) the length of the first formationperiod 1926-1929 will be four years rather than seven. Table 1 replicates and extends Table1 from Fama-Macbeth (1973) and provides information on the formation, estimation andtesting periods. Notice that the sample the authors use in Fama-Macbeth (1973) is from1926 through 6/1968. I extend their sample through 12/2010. The number of securities inthe formation, estimation and testing periods are slightly different from those in Fama andMacbeth (1973) mostly due to changes in the CRSP dataset over the last few decades.

6I use o to denote values estimated from a regression and distinguish estimates from true values. In thelimit as the sample gets infinitely large these estimates converge to the true values of the coefficients. Thusγ0 is an estimate of γ0, the true value of the coefficient. I use o to denote sample averages and o to denoterandom variables.

4

! ! ! ! ! !!! 1 2 3 4 5! ! ! ! ! !Portfolio!formation!period 1926629 1927633 1931637 1935641 1939645Initial!estimation!period 1930634 1934638 1938642 1942646 1946650Testing!period 1935638 1939642 1943646 1947650 1951654No.!of!securities!available 711 779 807 921 1024No.!of!securities!meeting ! ! ! ! !!!data!requirement 415 581 608 717 760! ! ! ! ! !! ! ! ! ! !!! 1 2 3 4 !! ! ! ! ! !Portfolio!formation!period 1943649 1947653 1951657 1955661 !Initial!estimation!period 1950654 1954658 1958662 1962666 !Testing!period 1955658 1959662 1963666 1967668 !No.!of!securities!available 1062 1071 1189 1284 !No.!of!securities!meeting ! ! ! ! !!!data!requirement 823 869 882 863 !! ! ! ! ! !! ! ! ! ! !!! 1 2 3 4 5! ! ! ! ! !Portfolio!formation!period 1959665 1963669 1967673 1971677 1975681Initial!estimation!period 1966670 1970674 1974678 1978682 1982686Testing!period 1971674 1975678 1979682 1983686 1987690No.!of!securities!available 1339 1518 1568 1488 1469No.!of!securities!meeting ! ! ! ! !!!data!requirement 827 928 1074 1105 978! ! ! ! ! !! ! ! ! ! !!! 1 2 3 4 5! ! ! ! ! !Portfolio!formation!period 1979685 1983689 1987693 1991697 1995601Initial!estimation!period 1986690 1990694 1994698 1998602 2002606Testing!period 1991694 1995698 1999602 2003606 2007610No.!of!securities!available 1565 2176 2429 2024 2005No.!of!securities!meeting ! ! ! ! !!!data!requirement 899 951 1011 1094 1239

TABLE!1PORTFOLIO!FORMATION,!ESTIMATION!AND!TESTING!PERIODS

PERIODS

PERIODS

PERIODS

PERIODS

Table 1

5

3 Results

3.1 Summary statistics

Most of the results will consist of producing different versions of the tables from Fama-Macbeth (1973). In describing the results I will limit the discussion to and show summaryresults for 1) the original Fama-Macbeth (1973) tables which I extend to include data for1968-2010; I will label the resulting tables, Table #a, 2) a version of the tables using boththe value-weighted NYSE market portfolio proxy and value-weighted averages of the under-lying securities βi and speitq to construct the corresponding portfolio-level estimates for thetwenty portfolios (labelled Table #d), 3) the original Fama and Macbeth (1973) tables butwith the twenty-five dual-sort portfolios (labelled Table #e), and 4) the results from usingboth the value-weighted NYSE market portfolio proxy and a value-weighted average of theunderlying securities βi and speitq to construct the twenty-five dual-sort portfolios estimates(labelled Table #h). I will include other variations of the tables in the Appendix.

First, I replicate and extend Table 2 from Fama and Macbeth (1973) below. The proxyfor the market portfolio is the equal-weighted NYSE index and the test portfolios are thetwenty beta-sorted portfolios. I obtain point estimates very similar to those in Fama andMacbeth (1973) for the 1926-1968 period. I display the result on Table 2a, below. In par-ticular, the portfolio betas range from 0.24 for the first quantile to 1.56 for the twentiethquantile. Also notice that for the first quantile the average beta increases from 0.24 to 0.66for the estimation periods 1934-38 through 1966-70. But then it monotonically decreasesfor the subsequent estimation periods 1974-78 to 2002-06 from 0.56 to 0.23. This may behinting that the nature of the betas have changed at lowest portfolio beta-quantile betweenthe time period 1926-1968 (used in the Fama and Macbeth; 1973) and the subsequent timeperiod 1968-2010. Although I cannot rule out small sample bias as the cause of these results,time-varying betas may also be part of the reason.

In order to determine how robust these estimates are I produce the following variationsof Table 2. First, in Table 2d (of the Appendix), I show the resulting table when I use boththe value-weighted NYSE market portfolio proxy and value-weighted averages of the under-lying securities βi and speitq to construct the corresponding portfolio estimates. I calculatethe percentage difference between Table 2d and Table 2a and display the results graphicallyon Figure (1a), shown below. Along the x-axis are the seven statistics of interest in thefollowing order: the portfolio beta βp,t�1, the estimated standard error of the portfolio beta

spβp,t�1q, the square of the correlation between the portfolio return and the market portfolioproxy return rpRp, Rmq

2, the estimated standard deviation of the portfolio return spRpq, thestandard deviation of the residuals from regressing portfolio returns against market port-folio proxy returns spepq, the weighted-average of the standard deviations of the residualsfrom regressing each underlying security returns again the market portfolio proxy returnssp,t�1peiq, and spepq{sp,t�1peiq. The y-axis lists the respective portfolio. And the z-axis showsthe percentage deviations from Table 2a.

6

Statistics 1 2 3 4 5 6 7 8 9 101 1 1 1 1 1 1 1 1 11

0.2429 0.2938 0.3493 0.5820 0.6477 0.7326 0.7416 0.8639 0.8960 0.89700.2035 0.2229 0.1966 0.0828 0.0669 0.0421 0.0298 0.0150 0.0155 0.02670.8421 0.8421 0.8421 0.8421 0.8421 0.8421 0.8421 0.8421 0.8421 0.84210.0759 0.0944 0.0912 0.0931 0.1012 0.0949 0.1161 0.0998 0.0996 0.11590.0302 0.0283 0.0282 0.0267 0.0224 0.0256 0.0324 0.0231 0.0265 0.02680.0838 0.0838 0.0838 0.0838 0.0838 0.0838 0.0838 0.0733 0.0733 0.07330.3600 0.3372 0.3372 0.3191 0.2678 0.3056 0.3866 0.3149 0.3622 0.3652

1 1 1 1 1 1 1 1 1

0.2475 0.4370 0.6118 0.6406 0.7170 0.7622 0.9228 0.9761 0.9810 1.00400.0334 0.0035 0.0208 0.0045 0.0163 0.0105 0.0524 0.0437 0.0235 0.01650.7474 0.7927 0.8047 0.8439 0.8890 0.8508 0.9034 0.9077 0.9265 0.95100.03551 0.0396 0.0527 0.0429 0.0466 0.0488 0.0540 0.0547 0.0619 0.05800.01784 0.0180 0.0233 0.0169 0.0155 0.0189 0.0168 0.0166 0.0168 0.01280.0542 0.0542 0.0544 0.0542 0.0544 0.0544 0.0544 0.0544 0.0544 0.05440.3294 0.3326 0.4281 0.3128 0.2852 0.3465 0.3081 0.3050 0.3084 0.2358

1 1 1 1 1 1 1 1 1

0.4597 0.5366 0.6250 0.6502 0.7220 0.7432 0.8038 0.8287 0.8420 0.89770.0297 0.0080 0.0283 0.0398 0.0362 0.0393 0.0304 0.0399 0.0392 0.03040.6149 0.6981 0.7725 0.8659 0.9095 0.8965 0.9034 0.9403 0.9430 0.92470.02409 0.0219 0.0269 0.0286 0.0317 0.0312 0.0338 0.0388 0.0372 0.03630.01495 0.0120 0.0128 0.0105 0.0095 0.0100 0.0105 0.0095 0.0089 0.01000.0399 0.0399 0.0399 0.0399 0.0399 0.0399 0.0399 0.0399 0.0399 0.03990.3744 0.3007 0.3211 0.2624 0.2391 0.2512 0.2633 0.2376 0.2221 0.2496

1 1 1 1 1 1 1 1 1

0.4394 0.5873 0.7484 0.7549 0.7627 0.8164 0.9793 0.9823 0.9838 1.01600.0224 0.0222 0.0568 0.0489 0.0119 0.0049 0.0145 0.0067 0.0080 0.01000.7957 0.8430 0.8760 0.8900 0.9188 0.9152 0.9360 0.9467 0.9251 0.93220.0335 0.0350 0.0359 0.0338 0.0361 0.0373 0.0405 0.0418 0.0423 0.04200.01514 0.0139 0.0127 0.0112 0.0103 0.0109 0.0102 0.0097 0.0116 0.01100.0498 0.0498 0.0498 0.0498 0.0498 0.0498 0.0498 0.0498 0.0498 0.04980.3040 0.2787 0.2539 0.2251 0.2064 0.2182 0.2056 0.1939 0.2321 0.2197

1 1 1 1 1 1 1 1 1

0.6101 0.6206 0.6965 0.7659 0.7854 0.8456 0.8679 0.9535 0.9550 0.95710.0391 0.0154 0.0220 0.0189 0.0200 0.0127 0.0136 0.0379 0.0284 0.02410.7802 0.7152 0.7641 0.8635 0.8874 0.9128 0.9263 0.9451 0.9560 0.94580.04056 0.0388 0.0415 0.0456 0.0468 0.0450 0.0539 0.0501 0.0553 0.04940.01901 0.0207 0.0201 0.0169 0.0157 0.0133 0.0146 0.0117 0.0116 0.01150.0694 0.0694 0.0694 0.0694 0.0694 0.0694 0.0694 0.0694 0.0694 0.06940.2740 0.2981 0.2903 0.2429 0.2262 0.1917 0.2106 0.1690 0.1673 0.1659

0.5587 0.5745 0.6114 0.6488 0.7423 0.7487 0.7946 0.8527 0.8551 0.87230.0368 0.0270 0.0121 0.0200 0.0227 0.0295 0.0202 0.0196 0.0110 0.01550.7538 0.7835 0.8032 0.9065 0.9078 0.9223 0.9111 0.9169 0.9446 0.93080.05202 0.0493 0.0488 0.0490 0.0501 0.0529 0.0561 0.0521 0.0619 0.05890.02581 0.0230 0.0217 0.0150 0.0152 0.0147 0.0167 0.0150 0.0146 0.01550.0595 0.0595 0.0595 0.0595 0.0595 0.0595 0.0595 0.0595 0.0595 0.05950.4338 0.3858 0.3641 0.2516 0.2558 0.2477 0.2809 0.2526 0.2448 0.2604

1 1 1 1 1 1 1 1 1

0.5491 0.6146 0.6556 0.6696 0.7329 0.7536 0.7905 0.8103 0.8618 0.91540.0286 0.0165 0.0143 0.0173 0.0149 0.0135 0.0075 0.0119 0.0106 0.02320.6371 0.5766 0.7363 0.8325 0.8207 0.8695 0.9027 0.9324 0.9043 0.93740.03336 0.0291 0.0347 0.0391 0.0364 0.0393 0.0425 0.0422 0.0441 0.04640.0201 0.0189 0.0178 0.0160 0.0154 0.0142 0.0132 0.0110 0.0136 0.01160.0474 0.0474 0.0474 0.0474 0.0474 0.0474 0.0474 0.0474 0.0596 0.04740.4245 0.4001 0.3758 0.3383 0.3257 0.3001 0.2796 0.2316 0.2290 0.2450

1 1 1 1 1 1 1 1 1

0.4535 0.5258 0.6075 0.6612 0.7792 0.7859 0.8080 0.9175 1.0300 1.04700.0522 0.0681 0.0565 0.0310 0.0334 0.0341 0.0564 0.0306 0.0280 0.03110.2653 0.3506 0.4916 0.6653 0.7747 0.7783 0.7853 0.8352 0.8238 0.85340.02637 0.0274 0.0322 0.0315 0.0363 0.0366 0.0403 0.0369 0.0429 0.04920.0226 0.0220 0.0229 0.0182 0.0172 0.0172 0.0187 0.0150 0.0180 0.01890.0367 0.0367 0.0367 0.0367 0.0367 0.0367 0.0367 0.0367 0.0457 0.03670.6165 0.6011 0.6255 0.4964 0.4700 0.4700 0.5096 0.4089 0.3942 0.5140

1 1 1 1 1 1 1 1 1

0.2567 0.3555 0.4157 0.5775 0.6683 0.7887 0.8396 0.8742 0.9014 0.93920.0248 0.0218 0.0228 0.0592 0.0481 0.0264 0.0552 0.0217 0.0156 0.02020.2612 0.1635 0.4095 0.4788 0.6937 0.7833 0.6700 0.9215 0.8208 0.84750.02507 0.0328 0.0333 0.0421 0.0392 0.0432 0.0460 0.0474 0.0456 0.05150.02155 0.0300 0.0256 0.0304 0.0217 0.0201 0.0264 0.0133 0.0193 0.02010.0572 0.0568 0.0572 0.0572 0.0549 0.0549 0.0549 0.0549 0.0554 0.05540.3768 0.5278 0.4475 0.5314 0.3948 0.3666 0.4816 0.2421 0.3486 0.3627

1 1 1 1 1 1 1 1 1

0.2320 0.2843 0.3283 0.4210 0.6107 0.6318 0.6396 0.7380 0.8787 0.92050.0205 0.0203 0.0218 0.0724 0.0207 0.0507 0.0503 0.0744 0.0050 0.01890.4433 0.3691 0.5467 0.6055 0.7747 0.7985 0.8758 0.9157 0.8708 0.90360.02464 0.0244 0.0287 0.0282 0.0329 0.0313 0.0305 0.0345 0.0341 0.03660.01839 0.0194 0.0193 0.0177 0.0156 0.0141 0.0107 0.0100 0.0122 0.01140.0446 0.0446 0.0446 0.0446 0.0446 0.0446 0.0447 0.0447 0.0447 0.04470.4126 0.4351 0.4333 0.3976 0.3504 0.3154 0.2400 0.2239 0.2735 0.2540

Portfolios1for1Estimation1Period11998=02






TABLE12a:1Equal=Weighted1NYSE1Market1Portfolio111111111+1111111201Single=Sort1Test1Portfolios1Built1Using1Equal=Weighted1SecuritiesSAMPLE1STATISTICS1FOR1FOUR1SECLECTED1ESTIMATION1PERIODS1(test1portfolios11=10)





�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)

sp,t�1(ei)s(ep)/sp,t�1(ei)

�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


7

1 1 1 1 1 1 1 1 1Statistics 11 12 13 14 15 16 17 18 19 20

1 1 1 1 1 1 1 1 1

0.9502 1.0090 1.0970 1.1640 1.1920 1.2490 1.3510 1.3570 1.3880 1.46100.0170 0.0147 0.0249 0.0586 0.0614 0.0677 0.0577 0.0703 0.0574 0.02180.8421 0.8421 0.8421 0.8421 0.8421 0.8421 0.8421 0.8421 0.8421 0.84210.1149 0.1065 0.1097 0.1177 0.1248 0.1148 0.1233 0.1237 0.1215 0.14030.0221 0.0251 0.0288 0.0311 0.0333 0.0298 0.0324 0.0314 0.0276 0.03670.0733 0.0733 0.0851 0.0851 0.0851 0.0851 0.0851 0.0851 0.0851 0.08510.3017 0.3419 0.3382 0.3655 0.3916 0.3494 0.3799 0.3687 0.3243 0.4309

1 1 1 1 1 1 1 1 1

1.0410 1.1320 1.2130 1.2240 1.2330 1.3220 1.3270 1.3660 1.3710 1.55200.0186 0.0139 0.0238 0.0244 0.0089 0.0077 0.0247 0.0154 0.0246 0.04780.9529 0.9328 0.9151 0.8908 0.9134 0.9488 0.9102 0.8157 0.9715 0.84590.0654 0.0693 0.0755 0.0814 0.0832 0.0730 0.0837 0.1049 0.0862 0.11980.0142 0.0180 0.0220 0.0269 0.0245 0.0165 0.0251 0.0450 0.0145 0.04700.0544 0.0527 0.0544 0.0527 0.0527 0.0527 0.0527 0.0527 0.0527 0.05270.2608 0.3408 0.4041 0.5107 0.4647 0.3136 0.4760 0.8545 0.2760 0.8927

1 1 1 1 1 1 1 1 1

0.9478 1.0360 1.0480 1.1070 1.1910 1.2940 1.3900 1.4030 1.5570 1.56000.0258 0.0069 0.0320 0.0069 0.0097 0.0243 0.0337 0.0219 0.0537 0.04140.9531 0.9411 0.9171 0.9382 0.9473 0.9327 0.9452 0.9048 0.8850 0.79960.0377 0.0411 0.0454 0.0420 0.0447 0.0460 0.0523 0.0509 0.0554 0.05950.0082 0.0100 0.0131 0.0105 0.0103 0.0119 0.0122 0.0157 0.0188 0.02660.0430 0.0430 0.0399 0.0399 0.0430 0.0430 0.0430 0.0430 0.0430 0.04300.1899 0.2322 0.3272 0.2617 0.2387 0.2775 0.2845 0.3656 0.4372 0.6200

1 1 1 1 1 1 1 1 1

1.0740 1.1140 1.1590 1.1650 1.2000 1.2180 1.2410 1.2460 1.4770 1.49900.0285 0.0196 0.0191 0.0149 0.0229 0.0158 0.0064 0.0613 0.0248 0.05410.9387 0.9486 0.9428 0.8992 0.9463 0.9338 0.9236 0.9052 0.9175 0.86580.0462 0.0450 0.0487 0.0458 0.0490 0.0495 0.0490 0.0564 0.0567 0.05760.0114 0.0102 0.0117 0.0145 0.0114 0.0127 0.0135 0.0174 0.0163 0.02110.0498 0.0517 0.0517 0.0517 0.0498 0.0501 0.0517 0.0501 0.0501 0.05010.2295 0.1974 0.2255 0.2816 0.2279 0.2545 0.2622 0.3467 0.3249 0.4215

1 1 1 1 1 1 1 1 1

1.0110 1.0250 1.0360 1.0390 1.0470 1.1130 1.1260 1.1500 1.3020 1.45000.0314 0.0269 0.0194 0.0202 0.0251 0.0363 0.0423 0.0571 0.0287 0.04990.9426 0.9579 0.9439 0.9645 0.9495 0.9299 0.9402 0.9294 0.9407 0.93690.0565 0.0519 0.0587 0.0617 0.0562 0.0631 0.0641 0.0660 0.0672 0.07160.0135 0.0107 0.0139 0.0116 0.0126 0.0167 0.0157 0.0175 0.0164 0.01800.0694 0.0694 0.0598 0.0598 0.0598 0.0598 0.0598 0.0598 0.0590 0.05900.1949 0.1534 0.2323 0.1941 0.2110 0.2791 0.2619 0.2929 0.2773 0.3047

0.8786 0.9812 1.0080 1.0760 1.0900 1.0960 1.1040 1.1930 1.2510 1.43300.0190 0.0215 0.0161 0.0200 0.0275 0.0305 0.0280 0.0173 0.0172 0.02260.9353 0.9582 0.9569 0.9460 0.9469 0.9540 0.9671 0.9482 0.9084 0.92170.0636 0.0643 0.0692 0.0717 0.0712 0.0700 0.0803 0.0780 0.0900 0.09270.0162 0.0132 0.0144 0.0167 0.0164 0.0150 0.0146 0.0178 0.0272 0.02590.0595 0.0595 0.0564 0.0564 0.0564 0.0564 0.0564 0.0564 0.0564 0.05640.2720 0.2211 0.2543 0.2952 0.2905 0.2659 0.2581 0.3145 0.4827 0.4596

1 1 1 1 1 1 1 1 1

0.9296 0.9563 0.9936 1.0270 1.0430 1.1120 1.1530 1.2480 1.2560 1.51400.0187 0.0179 0.0091 0.0094 0.0189 0.0113 0.0209 0.0182 0.0536 0.02360.8934 0.9298 0.9114 0.9356 0.9238 0.9094 0.9343 0.8893 0.8347 0.90060.0492 0.0475 0.0462 0.0489 0.0471 0.0492 0.0553 0.0477 0.0592 0.06430.0161 0.0126 0.0138 0.0124 0.0130 0.0148 0.0142 0.0159 0.0241 0.02030.0474 0.0474 0.0596 0.0474 0.0596 0.0596 0.0596 0.0596 0.0594 0.05940.3396 0.2656 0.2310 0.2621 0.2182 0.2488 0.2379 0.2663 0.4046 0.3408

1 1 1 1 1 1 1 1 1

1.0610 1.0850 1.0920 1.0990 1.1190 1.1340 1.1790 1.1940 1.2340 1.32800.0142 0.0076 0.0097 0.0117 0.0128 0.0067 0.0183 0.0180 0.0296 0.03500.9021 0.7938 0.8482 0.7453 0.8128 0.8187 0.8754 0.7588 0.5742 0.80910.0440 0.0462 0.0518 0.0541 0.0441 0.0509 0.0500 0.0594 0.0634 0.07080.0138 0.0210 0.0202 0.0273 0.0191 0.0217 0.0177 0.0292 0.0414 0.03100.0367 0.0367 0.0457 0.0367 0.0457 0.0457 0.0457 0.0457 0.0457 0.04570.3754 0.5726 0.4413 0.7453 0.4176 0.4742 0.3862 0.6384 0.9051 0.6773

1 1 1 1 1 1 1 1 1

0.9516 0.9613 1.0310 1.0490 1.1770 1.2470 1.2640 1.2880 1.3370 1.55700.0066 0.0270 0.0297 0.0505 0.0402 0.0294 0.0347 0.0281 0.0248 0.05940.8129 0.8314 0.9045 0.8686 0.8904 0.8405 0.9068 0.9060 0.8271 0.81060.0539 0.0516 0.0582 0.0622 0.0640 0.0732 0.0692 0.0682 0.0766 0.08250.0233 0.0212 0.0180 0.0225 0.0212 0.0292 0.0211 0.0209 0.0318 0.03590.0461 0.0563 0.0461 0.0563 0.0461 0.0461 0.0461 0.0461 0.0461 0.04610.5059 0.3762 0.3902 0.4005 0.4593 0.6337 0.4579 0.4532 0.6903 0.7784

1 1 1 1 1 1 1 1 1

0.9931 1.0500 1.0870 1.1060 1.1490 1.2170 1.2770 1.3360 1.3710 1.42900.0237 0.0134 0.0082 0.0248 0.0128 0.0319 0.0322 0.0081 0.0054 0.00960.8741 0.8719 0.8852 0.8781 0.8971 0.8796 0.8819 0.8871 0.8786 0.84990.0398 0.0462 0.0437 0.0423 0.0477 0.0509 0.0504 0.0508 0.0488 0.05820.0141 0.0165 0.0148 0.0148 0.0153 0.0177 0.0173 0.0171 0.0170 0.02260.0434 0.0434 0.0351 0.0352 0.0352 0.0354 0.0354 0.0354 0.0354 0.03530.3255 0.3811 0.4226 0.4197 0.4356 0.4990 0.4897 0.4826 0.4804 0.6392









TABLE12a:1Equal=Weighted1NYSE1Market1Portfolio111111111+1111111201Single=Sort1Test1Portfolios1Built1Using1Equal=Weighted1SecuritiesSAMPLE1STATISTICS1FOR1FOUR1SECLECTED1ESTIMATION1PERIODS1(test1portfolios111=20)1111



�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


8

(a) This figure displays the percentage difference need spacebetween Table 2d and Table 2a. In Table 2d, I use theneedvalue-weighted NYSE as a market portfolio proxy and andI use a value-weighted of the underlying securities βi and

and speitq to construct βp,t�1 and sp,t�1peiq for the twentytwenty portfolios. Table 2a is the original table from FamaFama-Macbeth (1973).

(b) This figure displays the percentage difference betweenTable 2e and Table 2a. In Table 2e, I use the equal-weightedNYSE as a market portfolio proxy and I use the equal-weighted underlying securities βi and speitq to construct

βp,t�1 and sp,t�1peiq for the twenty-five double-sort port-folios. To calculate the percentage differences I use porfolios1, 5, 10, 16 and 20 from Fama-MacBeth (1973) and the cor-responding beta-quintile of the 5 � 5 test portfolios.

(c) This figure displays the percentage difference betweenTable 2h and Table 2a. In Table 2h, I use the value-weightedNYSE as a market portfolio proxy and I use value-weightedunderlying securities βi and speitq to construct βp,t�1 andsp,t�1peiq for the twenty-five double-sort portfolios. To cal-culate the percentage differences I use porfolios 1, 5, 10, 16and 20 from Fama-MacBeth (1973) and the correspondingbeta-quintile of the 5 � 5 test portfolios.

Figure 1: The x-axis show the following statistics: 1) the portfolio beta βp,t�1, 2) the estimated standard error

of the portfolio beta spβp,t�1q, 3) the square of the correlation between the portfolio return and the marketportfolio proxy return rpRp, Rmq2, 4) the estimated standard deviation of the portfolio return spRpq, 5) thestandard deviation of the residuals from regressing portfolio returns against market portfolio proxy returnsspepq, 6) the weighted-average of the standard deviations of the residuals from regressing each underlyingsecurity returns again the market portfolio proxy returns sp,t�1peiq, and 7) spepq{sp,t�1peiq. The y-axis liststhe respective portfolio. And the z-axis shows the percentage deviations from Table 2a.

One of the most striking features of Figure (1a) is that statistics 7, spepq{sp,t�1peiq seemsto be much larger when the market proxy is the value-weighted NYSE compared to whenan equal-weighted NYSE index is used. This holds for all portfolio quantiles. In particular,this statistics increases by 50-150%. This implies that the equal-weighted NYSE is betterat predicting the twenty beta-sorted portfolios of Fama and Macbeth (1973) than the value-weighted NYSE. Indeed, this is confirmed by statistics 3, rpRp, Rmq

2, which is a measureof the goodness of fit. We can observe that the difference between rpRp, Rmq

2 from Table2d and Table 2a is slightly negative for all twenty portfolios; thus the fit is slightly worsewhen I use the value-weighted NYSE as a proxy for the market portfolio. Notice that theportfolio betas (statistics 1) are slightly greater on Table 2d than Table 2a. Recall that

βx,y �covpx,yqσ2y

and corrpx, yq � covpx,yqσxσy

. Since the magnitude of the correlation between Rp

and Rm is smaller on Table 2d than on Table 2a and since βp,t�1 is larger on Table 2d thanon Table 2a, it may be that the volatility in the test portfolio returns is larger when we usethe value-weighted NYSE as proxy for the market portfolio, that the value-weighted NYSEis less volatile than the equal-weighted NYSE and that the covariance between the portfolioreturns and the market proxy returns increases. I do find that the estimated standard de-viation of the test portfolio returns (statistics 4) are a bit larger on Table 2d. Later, I willalso show that the equal-weighted NYSE has a greater standard deviation than the value-weighted NYSE. I find that on average the equal-weighted NYSE portfolio has a standarddeviation that is twenty-six percent greater than that of the value-weighted NYSE portfolio.Thus, using the value-weighted NYSE market portfolio proxy leads to larger standard errorsfor the portfolio betas (statistics 2 is increasingly larger as the beta-quantile increases), andlower covariance between the test portfolio returns and the proxy for the market returns.But since the value-weighted NYSE is less volatile than the equal-weighted NYSE the levelof the portfolio betas increases a bit but the goodness of fit for the regression of the testportfolio returns against the market proxy returns decreases slightly.

I then repeat the exercise with the twenty-five portfolios based on a dual-sort of betas andstandard deviation of the returns on the underlying securities (the results are in Tables 2e,2f, 2g and 2h). Table 2h is displayed below. I also include the percentage difference be-tween Table 2e and Table 2a on Figure (1b). On Figure (1b) we can see that the differencesbetween Tables 2e and 2a are less systematic. Nonetheless, the change in the statistics 7,spepq{sp,t�1peiq, is more than ten percent for most of the portfolios. Figure (1c) shows thedifference between Table 2h and Table 2a. Here the results are qualitatively similar to thoseof Figure (1a). However, the magnitude of statistics 5, spepq, and statistics 7, spepq{sp,t�1peiq,are much greater. This hints that model (1) will have difficulties pricing the portfolio returnswhen the test portfolios estimates are constructed using a value-weighted approach and/orwhen the test portfolios are constructed from a dual sort on betas and standard deviationof the residuals of the underlying securities.

10

Statistics 1 2 3 4 5 6 7 8 9 10 11 12 131 1 1 1 1 1 1 1 1 1 1 1 11

0.1982 0.2179 0.3416 0.3583 0.5905 0.6921 0.7318 0.7658 0.8538 0.8645 0.9063 0.9174 0.94490.3208 0.2990 0.2972 0.2452 0.1587 0.1563 0.1640 0.1504 0.1740 0.1670 0.1778 0.1844 0.21740.4401 0.4401 0.4401 0.4401 0.4401 0.4401 0.4401 0.4401 0.4401 0.4401 0.4401 0.4401 0.44010.1490 0.0855 0.0868 0.1178 0.1268 0.1102 0.0955 0.1087 0.1162 0.1596 0.1121 0.1000 0.13250.1115 0.0508 0.0452 0.0737 0.0943 0.0571 0.0488 0.0590 0.0754 0.1208 0.0636 0.0503 0.06770.0436 0.0436 0.0436 0.0436 0.0436 0.0436 0.0436 0.0436 0.0436 0.0436 0.0593 0.0593 0.05932.5550 1.1640 1.0360 1.6890 2.1610 1.3100 1.1190 1.3540 1.7280 2.7700 1.0710 0.8470 1.1420

1 1 1 1 1 1 1 1 1 1 1 1

0.5582 0.6192 0.8563 1.0730 1.1020 1.1220 1.1390 1.1730 1.2260 1.3720 1.4600 1.5730 1.63900.1171 0.0267 0.0755 0.1247 0.1106 0.0688 0.0533 0.0413 0.0208 0.0361 0.0531 0.0880 0.10470.4898 0.7589 0.1020 0.1930 0.6181 0.7678 0.6575 0.7801 0.6143 0.6204 0.8232 0.5185 0.65460.05024 0.0428 0.0805 0.1170 0.0678 0.0494 0.0632 0.0488 0.0644 0.0795 0.0506 0.0616 0.06290.03589 0.0210 0.0763 0.1051 0.0419 0.0238 0.0370 0.0229 0.0400 0.0490 0.0213 0.0427 0.03690.0441 0.0441 0.0441 0.0441 0.0441 0.0441 0.0441 0.0441 0.0441 0.0441 0.0441 0.0540 0.05400.8135 0.4761 1.7300 2.3820 0.9498 0.5401 0.8385 0.5192 0.9067 1.1100 0.4822 0.7918 0.6842

1 1 1 1 1 1 1 1 1 1 1 1

0.4110 0.6066 0.7508 0.8363 0.8659 0.9766 1.0570 1.0650 1.1080 1.1430 1.1710 1.2300 1.25600.1141 0.0573 0.0258 0.0422 0.0492 0.0651 0.0449 0.0366 0.0317 0.0204 0.0223 0.0362 0.03940.5048 0.4156 0.4498 0.4648 0.3043 0.7522 0.6366 0.5915 0.4788 0.3736 0.7766 0.6463 0.63850.02798 0.0331 0.0309 0.0329 0.0353 0.0372 0.0459 0.0391 0.0455 0.0411 0.0397 0.0453 0.04440.01969 0.0253 0.0229 0.0241 0.0294 0.0185 0.0277 0.0250 0.0329 0.0325 0.0188 0.0270 0.02670.0440 0.0440 0.0440 0.0440 0.0440 0.0406 0.0440 0.0440 0.0400 0.0406 0.0440 0.0406 0.04060.4471 0.5754 0.5208 0.5467 0.6684 0.4565 0.6287 0.5671 0.8210 0.8005 0.4264 0.6639 0.6580

1 1 1 1 1 1 1 1 1 1 1 1

0.4092 0.4104 0.5256 0.5512 0.7272 0.7319 0.7516 0.7728 0.8975 0.9153 0.9633 0.9719 1.02000.0562 0.0713 0.0540 0.0514 0.0855 0.0803 0.0544 0.0462 0.0357 0.0375 0.0566 0.0477 0.05460.6912 0.6154 0.6353 0.5635 0.6025 0.6186 0.5762 0.5245 0.5787 0.5684 0.6314 0.5666 0.58410.03464 0.0385 0.0380 0.0471 0.0503 0.0431 0.0453 0.0548 0.0485 0.0581 0.0421 0.0541 0.06010.01925 0.0239 0.0229 0.0311 0.0317 0.0266 0.0295 0.0378 0.0315 0.0381 0.0256 0.0356 0.03870.0407 0.0407 0.0407 0.0407 0.0407 0.0407 0.0407 0.0407 0.0407 0.0445 0.0445 0.0445 0.04450.4726 0.5857 0.5631 0.7644 0.7786 0.6540 0.7238 0.9283 0.7729 0.8578 0.5754 0.8017 0.8714

1 1 1 1 1 1 1 1 1 1 1 1

0.5930 0.6672 0.7041 0.7730 0.7769 0.7876 0.8807 0.9703 0.9964 1.0040 1.0060 1.0510 1.05200.0810 0.0349 0.0411 0.0325 0.0413 0.0528 0.0262 0.0197 0.0206 0.0196 0.0429 0.0360 0.04050.6384 0.5769 0.5021 0.5893 0.5538 0.6901 0.7126 0.6112 0.5143 0.5143 0.6547 0.7050 0.71500.0416 0.0472 0.0468 0.0624 0.0786 0.0466 0.0487 0.0578 0.0687 0.0879 0.0516 0.0521 0.05890.02502 0.0307 0.0330 0.0400 0.0525 0.0260 0.0261 0.0361 0.0479 0.0613 0.0303 0.0283 0.03140.0568 0.0568 0.0568 0.0568 0.0568 0.0568 0.0549 0.0568 0.0568 0.0549 0.0568 0.0568 0.05680.4401 0.5399 0.5809 0.7036 0.9235 0.4568 0.4755 0.6345 0.8420 1.1160 0.5338 0.4978 0.5530

0.5693 0.6217 0.6304 0.8976 0.8982 0.9878 0.9972 1.0200 1.0230 1.0380 1.0490 1.0890 1.10100.0699 0.0563 0.0816 0.0260 0.0149 0.0482 0.0284 0.0384 0.0482 0.0468 0.0416 0.0399 0.04800.4594 0.6416 0.6117 0.5592 0.2604 0.7889 0.6028 0.6571 0.6362 0.3382 0.6228 0.7121 0.60430.05901 0.0495 0.0509 0.0481 0.0832 0.0544 0.0592 0.0542 0.0678 0.0875 0.0526 0.0863 0.07260.04339 0.0297 0.0317 0.0319 0.0716 0.0250 0.0373 0.0318 0.0409 0.0712 0.0323 0.0463 0.04560.0567 0.0567 0.0567 0.0567 0.0567 0.0567 0.0567 0.0567 0.0567 0.0567 0.0548 0.0567 0.05480.7652 0.5231 0.5591 0.5631 1.2620 0.4405 0.6583 0.5601 0.7207 1.2550 0.5891 0.8169 0.8331

1 1 1 1 1 1 1 1 1 1 1 1

0.6849 0.7125 0.7397 0.8273 0.9317 0.9394 0.9782 0.9830 0.9864 0.9921 1.0360 1.0400 1.05500.1051 0.0893 0.0447 0.0527 0.0659 0.0548 0.0503 0.0399 0.0312 0.0307 0.0417 0.0325 0.03530.3654 0.3523 0.5918 0.5097 0.5708 0.7124 0.7168 0.5956 0.5599 0.6552 0.7332 0.6233 0.49240.03032 0.0349 0.0410 0.0446 0.0596 0.0435 0.0419 0.0643 0.0495 0.0552 0.0507 0.0554 0.05770.02416 0.0281 0.0262 0.0312 0.0391 0.0233 0.0223 0.0409 0.0328 0.0324 0.0262 0.0340 0.04110.0405 0.0405 0.0405 0.0405 0.0405 0.0405 0.0508 0.0405 0.0405 0.0508 0.0405 0.0405 0.05080.5970 0.6942 0.6466 0.7721 0.9651 0.5766 0.4384 1.0100 0.8107 0.6373 0.6476 0.8406 0.8091

1 1 1 1 1 1 1 1 1 1 1 1

0.4070 0.5278 0.5906 0.6876 0.7468 0.8203 0.8437 0.9501 0.9575 0.9742 1.0330 1.0430 1.07600.0729 0.0592 0.0399 0.0797 0.1184 0.1089 0.0975 0.0850 0.0713 0.0404 0.0284 0.0222 0.01980.3238 0.3482 0.3427 0.6814 0.4674 0.6404 0.5992 0.2712 0.4709 0.3714 0.4689 0.5548 0.41160.02739 0.0322 0.0323 0.0330 0.0422 0.0377 0.0478 0.0619 0.0540 0.0602 0.0531 0.0541 0.06890.02252 0.0260 0.0262 0.0186 0.0308 0.0226 0.0302 0.0529 0.0393 0.0478 0.0387 0.0361 0.05290.0309 0.0309 0.0309 0.0309 0.0309 0.0415 0.0309 0.0309 0.0415 0.0309 0.0309 0.0309 0.03090.7279 0.8408 0.8469 0.6013 0.9959 0.5458 0.9774 1.7090 0.9470 1.5430 1.2500 1.1660 1.7090

1 1 1 1 1 1 1 1 1 1 1 1

0.3272 0.4392 0.4611 0.5011 0.6101 0.6710 0.7954 0.8357 0.8499 0.8874 0.8938 0.9211 0.94640.0686 0.0790 0.0568 0.0714 0.0462 0.0407 0.0681 0.0796 0.0547 0.0365 0.0310 0.0291 0.01850.0348 0.1797 0.1600 0.1763 0.1946 0.5741 0.2949 0.3972 0.3540 0.2386 0.4799 0.3274 0.48370.02105 0.0406 0.0500 0.0563 0.0724 0.0503 0.0541 0.0556 0.0831 0.0861 0.0567 0.0604 0.06660.02068 0.0368 0.0458 0.0511 0.0650 0.0328 0.0454 0.0432 0.0668 0.0751 0.0409 0.0496 0.04790.0256 0.0257 0.0256 0.0256 0.0256 0.0256 0.0256 0.0256 0.0256 0.0245 0.0245 0.0240 0.02560.8067 1.4320 1.7860 1.9940 2.5360 1.2800 1.7710 1.6860 2.6080 3.0600 1.6670 2.0680 1.8690

1 1 1 1 1 1 1 1 1 1 1 1

0.0828 0.1077 0.2610 0.4231 0.4888 0.5512 0.6108 0.7213 0.7237 0.7857 0.8590 0.9238 0.92610.0381 0.0634 0.0273 0.0250 0.0010 0.0216 0.0123 0.0349 0.0144 0.0049 0.0286 0.0448 0.00820.0001 0.1046 0.2943 0.5202 0.2919 0.5427 0.3186 0.4310 0.4856 0.2918 0.6270 0.4646 0.52820.02425 0.0274 0.0338 0.0462 0.0597 0.0337 0.0356 0.0409 0.0663 0.0579 0.0356 0.0464 0.05250.02425 0.0259 0.0284 0.0320 0.0502 0.0228 0.0294 0.0308 0.0475 0.0487 0.0217 0.0340 0.03610.0252 0.0252 0.0252 0.0250 0.0252 0.0252 0.0251 0.0250 0.0250 0.0250 0.0250 0.0250 0.03030.9636 1.0300 1.1280 1.2780 1.9950 0.9061 1.1710 1.2320 1.8990 1.9450 0.8682 1.3570 1.1910







TABLE12h:1Value=Weighted1NYSE1Market1Portfolio111111111+11111115x51Double=Sort1Test1Portfolios1Built1Using1Value=Weighted1SecuritiesSAMPLE1STATISTICS1FOR1FOUR1SECLECTED1ESTIMATION1PERIODS1(test1portfolios11=13)





�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


11

1 1 1 1 1 1 1 1 1 1 1 1Statistics 14 15 16 17 18 19 20 21 22 23 24 25

1 1 1 1 1 1 1 1 1 1 1 1

0.9547 1.0390 1.1280 1.1440 1.1450 1.2580 1.2950 1.3200 1.3360 1.3570 1.3810 1.44600.2182 0.2165 0.2396 0.2351 0.2510 0.2374 0.2175 0.2340 0.2355 0.3163 0.3473 0.53710.4401 0.4401 0.4401 0.4401 0.4401 0.4401 0.4401 0.4401 0.4401 0.4401 0.4401 0.44010.1470 0.1510 0.0854 0.0982 0.1589 0.1349 0.1567 0.1043 0.1381 0.1385 0.1505 0.13700.0893 0.0996 0.0425 0.0585 0.0774 0.0892 0.1022 0.0474 0.0740 0.0884 0.0893 0.07280.0593 0.0593 0.0593 0.0593 0.0436 0.0436 0.0593 0.0593 0.0593 0.0593 0.0593 0.07431.5050 1.6790 0.7165 0.9855 1.7750 2.0450 1.7220 0.7996 1.2460 1.4890 1.5040 0.9791

1 1 1 1 1 1 1 1 1 1 1 1

1.7020 1.7130 1.7190 1.7420 1.8540 1.8980 1.9220 1.9660 1.9960 2.0950 2.0990 2.13200.1000 0.0784 0.0687 0.0523 0.0946 0.0875 0.0739 0.0782 0.0726 0.0845 0.0945 0.11420.3510 0.4049 0.4960 0.5708 0.4910 0.4234 0.6489 0.6448 0.5338 0.3046 0.3594 0.40720.1023 0.0978 0.0756 0.0894 0.0758 0.0890 0.0868 0.0760 0.0981 0.1470 0.1295 0.10130.0824 0.0755 0.0537 0.0585 0.0541 0.0676 0.0515 0.0453 0.0670 0.1226 0.1037 0.07800.0540 0.0441 0.0540 0.0540 0.0540 0.0540 0.0540 0.0540 0.0540 0.0540 0.0522 0.05401.5260 1.7110 0.9941 1.0850 1.0020 1.2520 0.9532 0.8392 1.2400 2.2710 1.9850 1.4450

1 1 1 1 1 1 1 1 1 1 1 1

1.3070 1.4260 1.4760 1.4890 1.5240 1.7680 1.8000 1.9220 1.9520 2.0230 2.0530 2.13200.0466 0.0876 0.0683 0.0465 0.0582 0.1348 0.1314 0.1634 0.1593 0.1705 0.1395 0.14520.5516 0.4357 0.7375 0.5744 0.5572 0.5547 0.3723 0.4832 0.6462 0.4709 0.2259 0.25750.0521 0.0493 0.0575 0.0542 0.0468 0.0579 0.0639 0.0578 0.0581 0.0618 0.0776 0.08790.0349 0.0371 0.0295 0.0353 0.0311 0.0386 0.0506 0.0415 0.0345 0.0450 0.0682 0.07580.0440 0.0440 0.0406 0.0440 0.0406 0.0406 0.0406 0.0406 0.0440 0.0406 0.0406 0.04060.7925 0.8413 0.7257 0.8025 0.7663 0.9515 1.2460 1.0220 0.7841 1.1070 1.6810 1.8660

1 1 1 1 1 1 1 1 1 1 1 1

1.0380 1.0910 1.1030 1.1130 1.1410 1.1510 1.1980 1.2030 1.3030 1.4260 1.4430 1.46300.0438 0.0374 0.0310 0.0326 0.0298 0.0171 0.0291 0.0294 0.0506 0.0816 0.0645 0.06150.6395 0.6017 0.6944 0.5125 0.6516 0.5838 0.4858 0.6830 0.5883 0.6716 0.5748 0.33100.0562 0.0637 0.0465 0.0611 0.0597 0.0685 0.0675 0.0516 0.0515 0.0586 0.0670 0.07010.0337 0.0402 0.0257 0.0427 0.0352 0.0442 0.0484 0.0290 0.0331 0.0336 0.0437 0.05730.0407 0.0407 0.0445 0.0445 0.0445 0.0445 0.0445 0.0445 0.0445 0.0407 0.0445 0.05600.8281 0.9862 0.5779 0.9599 0.7920 0.9945 1.0890 0.6528 0.7437 0.8248 0.9824 1.0240

1 1 1 1 1 1 1 1 1 1 1 1

1.0810 1.0930 1.1290 1.2070 1.2490 1.2700 1.3000 1.3450 1.3660 1.4690 1.5040 1.53400.0392 0.0680 0.0622 0.0593 0.0578 0.0431 0.1072 0.0960 0.1081 0.1094 0.0933 0.09550.6716 0.5970 0.7995 0.7340 0.7619 0.6604 0.6130 0.7049 0.6437 0.7007 0.7474 0.55720.0708 0.0873 0.0578 0.0509 0.0605 0.0712 0.0904 0.0583 0.0625 0.0616 0.0657 0.08470.0406 0.0554 0.0259 0.0262 0.0295 0.0415 0.0562 0.0317 0.0373 0.0337 0.0330 0.05640.0549 0.0549 0.0549 0.0568 0.0549 0.0549 0.0549 0.0549 0.0549 0.0549 0.0549 0.05250.7396 1.0100 0.4713 0.4617 0.5377 0.7553 1.0240 0.5766 0.6792 0.6135 0.6013 1.0750

1.1600 1.1690 1.2170 1.3280 1.3940 1.4710 1.5130 1.5250 1.5710 1.7110 1.7440 1.75500.0445 0.0462 0.0416 0.0669 0.0810 0.0740 0.0775 0.0795 0.0601 0.0890 0.0950 0.05630.7271 0.5043 0.6860 0.6883 0.6612 0.7030 0.6547 0.6864 0.6290 0.4254 0.4166 0.54020.0724 0.1175 0.0611 0.0732 0.0822 0.0842 0.0886 0.0832 0.0811 0.0935 0.0935 0.09000.0378 0.0827 0.0342 0.0409 0.0479 0.0459 0.0521 0.0466 0.0494 0.0709 0.0714 0.06100.0548 0.0548 0.0548 0.0548 0.0548 0.0567 0.0548 0.0548 0.0548 0.0548 0.0548 0.05680.6906 1.5100 0.6248 0.7461 0.8736 0.8097 0.9503 0.8501 0.9015 1.2930 1.3030 1.0730

1 1 1 1 1 1 1 1 1 1 1 1

1.0610 1.0980 1.1120 1.1130 1.1830 1.2090 1.2680 1.3120 1.3400 1.3610 1.3800 1.42300.0354 0.0296 0.0437 0.0397 0.0187 0.0194 0.0396 0.0414 0.0743 0.1160 0.0860 0.09890.6705 0.4526 0.8265 0.5721 0.6735 0.5463 0.4173 0.5034 0.6800 0.5098 0.4208 0.39110.0503 0.0567 0.0542 0.0608 0.0556 0.0580 0.0628 0.0501 0.0716 0.0777 0.0691 0.09400.0289 0.0420 0.0226 0.0398 0.0318 0.0391 0.0479 0.0353 0.0405 0.0544 0.0526 0.07330.0508 0.0508 0.0508 0.0508 0.0405 0.0508 0.0508 0.0405 0.0508 0.0508 0.0508 0.04680.5681 0.8255 0.4446 0.7821 0.7851 0.7686 0.9426 0.8721 0.7974 1.0710 1.0340 1.5660

1 1 1 1 1 1 1 1 1 1 1 1

1.0950 1.0980 1.1340 1.1350 1.1540 1.1560 1.1580 1.1890 1.2500 1.2690 1.2940 1.33400.0150 0.0153 0.0111 0.0110 0.0198 0.0257 0.0339 0.0378 0.0204 0.0282 0.0563 0.13920.2586 0.3421 0.6510 0.2634 0.4532 0.2873 0.2210 0.6472 0.4352 0.2504 0.0811 0.19520.0582 0.0826 0.0579 0.0665 0.0643 0.0633 0.0875 0.0547 0.0625 0.0636 0.1025 0.08380.0501 0.0670 0.0342 0.0571 0.0475 0.0535 0.0772 0.0325 0.0470 0.0551 0.0982 0.07520.0309 0.0415 0.0415 0.0415 0.0415 0.0415 0.0415 0.0415 0.0415 0.0418 0.0415 0.04151.6200 1.6160 0.8244 1.3760 1.1460 1.2890 1.8610 0.7826 1.1330 1.3170 2.3680 1.8120

1 1 1 1 1 1 1 1 1 1 1 1

0.9817 0.9846 1.0790 1.0950 1.1150 1.1150 1.2020 1.2170 1.2700 1.3380 1.3430 1.38100.0265 0.0246 0.0394 0.0369 0.0493 0.0447 0.0550 0.0611 0.0631 0.0740 0.0823 0.11390.3217 0.1768 0.4313 0.6852 0.4890 0.2336 0.3710 0.4983 0.4563 0.3599 0.4320 0.20630.0671 0.0900 0.0637 0.0773 0.0764 0.1055 0.0877 0.0816 0.0742 0.1010 0.0973 0.11610.0553 0.0817 0.0480 0.0434 0.0546 0.0924 0.0696 0.0578 0.0547 0.0808 0.0733 0.10340.0240 0.0256 0.0240 0.0256 0.0245 0.0245 0.0240 0.0245 0.0245 0.0519 0.0245 0.02452.3080 3.1870 2.0050 1.6930 2.2240 3.7650 2.9040 2.3540 2.2280 1.5560 2.9870 4.2130

1 1 1 1 1 1 1 1 1 1 1 1

0.9979 1.0300 1.1240 1.1390 1.1470 1.2340 1.2400 1.2700 1.2780 1.2930 1.3220 1.63100.0204 0.0239 0.0535 0.0509 0.0070 0.0480 0.0603 0.0614 0.0613 0.0612 0.0546 0.18720.2256 0.2877 0.6932 0.6889 0.5344 0.4177 0.3149 0.6017 0.5947 0.6524 0.5531 0.34970.0576 0.0546 0.0358 0.0576 0.0545 0.0524 0.0604 0.0421 0.0511 0.0578 0.0670 0.06960.0507 0.0461 0.0199 0.0321 0.0372 0.0400 0.0500 0.0266 0.0325 0.0341 0.0448 0.05610.0303 0.0303 0.0303 0.0303 0.0303 0.0303 0.0303 0.0305 0.0303 0.0486 0.0303 0.03051.6730 1.5210 0.6550 1.0600 1.2270 1.3200 1.6470 0.8716 1.0730 0.7014 1.4780 1.8390









TABLE12h:1Value=Weighted1NYSE1Market1Portfolio111111111+11111115x51Double=Sort1Test1Portfolios1Built1Using1Value=Weighted1SecuritiesSAMPLE1STATISTICS1FOR1FOUR1SECLECTED1ESTIMATION1PERIODS1(test1portfolios114=25)111



�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


12

3.2 Cross-sectional regressions

The most important table of Fama-Macbeth (1973) is arguably Table 3. I replicate theirresults below, in Table 3a. The table shows the results from the cross-sectional regression

Rp � γ0t � γ1tβp � γ2tβ2p � γ3tsppeiq � ηp

Recall that the cross-sectional regression is done each month of the testing period and theestimates displayed on the table are the corresponding averages for the testing period ofinterest. I calculate all the statistics displayed in the table using the approach of Fama andMacBeth (1973)7. Panel A displays the results from the cross-sectional regression of thetest portfolios against a constant and the proxy for the market portfolio returns. For the1935-6/1968, 7/1968-2010, and 1935-2010 testing periods I find ¯γ1 � 84bps, ¯γ1 � 36bps, and¯γ1 � 57bps (respectively). These values are all highly significant with t-statistics greaterthan 2. Overall , I find that ¯γ1, which in this practical test of the CAPM should correspondto the excess return of the market portfolio on the portfolio with zero beta with respect tothe market, is positive for almost all the testing periods. In Panel B, the first three regressorsare included in the regression specification. The aforementioned results do no change muchbut I find that ¯γ2 is negative ( ¯γ2 � �24bps for the 1935-2010 testing period) and is notsignificant (t-statistics=�1.2). Panel C uses the first two as well as the fourth regressor.Here, we can see that ¯γ0 and ¯γ1 have point estimates very similar to those in panels A andB. However, ¯γ1 seems to lose some of its significance as the t-statistics for these estimatesare rarely greater than 2. ¯γ3 is not significant in any of the testing periods. Panel D includesall four regressors and is the proposed test of the CAPM, conditional on the equal-weightedNYSE being the market portfolio, conditional on market efficiency and conditional on theassumptions laid out in the introduction (such as normality). Here, I find that ¯γ1 � 1.15% onaverage per month for the 1935-6/1968 testing period and ¯γ1 � 88bps on average per monthfor the full sample (1935-2010). In both cases the t-statistics is above 1.90. ¯γ2 and ¯γ3 areoverall not significant although ¯γ3 often has point estimates with rather large magnitudes. Inall four panels the average R2 (which is listed in the column labelled r2) remains around 0.30.

The results presented thus far are similar to those found in Fama and Macbeth (1973).With an equal-weighted NYSE portfolio as the proxy for the market portfolio and with testportfolios constructed from a beta-sort using equal-weighted underlying securities βi, I findlittle evidence of non-linear dependence on βp and little evidence that idiosyncratic risk asmeasured by sppeiq is priced. However, when I use the 5 � 5 dual sort test portfolios (whilemaintaining the same market portfolio proxy and the same method of constructing the port-folios estimates using the equal weighting of the underlying securities estimates) much ofthose results no longer hold. Indeed, on Table 3e we can first notice that in Panel A pointestimates for ¯γ1 are similar to those displayed on Table 3a, and the t-statistics are very similaras well. Indeed, for the 1935-6/1968 testing period the t-statistics is 2.61, for the 7/1968-2010testing period the t-statistics is 1.40 and for the 1935-2010 testing period the t-statistics is2.84. For these three testing periods the estimates I find are ¯γ1 � 86bps, 36bps, and 58bps(respectively). Thus, as in Panel A of Table 3a, we observe a deterioration of the significance

7In particular, ρM pγjq is the first-order autocorrelation for γjt while ρ0pγjq is the first-order autocorrela-tion for γjt with the additional assumption that the mean of γjt is zero (that is ρ0pγjt, ˆγjt�1q � Erγjt � ˆγjt�1sq

13

of the estimate for the testing periods subsequent to those used in Fama-MacBeth (1973).In Panel B of Table 3e, where I include the additional regressor, β2

p , I find that ¯γ1 loses muchof its significance. The t-statistics are 0.59, 1.56 and 1.63 for the 1935-6/1968, 7/1968-2010and 1935-2010 testing periods (respectively). Furthermore, the magnitude of the estimate ishalved for the 1935-6/1968 testing period (32bps) but trebles for the 7/1968-2010 testing pe-riod (96bps). In Panel C, the regressions include the measure of idiosyncratic risk sppeiq. Asa result, the estimates ¯γ1 lose much of their significance and the estimates for ¯γ3 are highlysignificant for the testing periods within 1935-6/1968. Indeed, the t-statistics are 0.52, 0.32,0.59 for ¯γ1 and 2.68, 0.80, 2.09 for ¯γ3 (respectively for the 1935-6/1968, 7/1968-2010 and1935-2010 testing periods). The most relevant results are in Panel D, which shows that whenI include all of the regressors, ¯γ3 remains highly significant. In particular, for the full testingperiod used in Fama-MacBeth (1973)8 the t-statistics for ¯γ1 is only 1.61 while correspondingt-statistics for ¯γ3 is 3.08. Furthermore, for the 7/1968-2010 and 1935-2010 testing periods, Ifind tp ¯γ1q � tp ¯γ3q � 1.36 and tp ¯γ1q � 2.03 tp ¯γ3q � 2.77. Conditional on market efficiency,normality of the distribution of portfolio returns, risk-aversion and common knowledge, theselast results would imply that idiosyncratic risk as measured by sppeiq is priced.

8The 1935-6/1968 testing period.

14

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Perio

d!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!A:

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

193516/68

0.0063

0.0084

11

0.0049

0.0360

0.0659

11

0.0047

0.0098

11

3.4760

2.5460

11

2.7480

0.3051

0.3016

1935145

0.0041

0.0163

11

0.0040

0.0485

0.0974

11

0.0039

10.047

01

10.9753

1.9160

11

0.9417

0.2945

0.2914

1946155

0.0084

0.0028

11

0.0075

0.0258

0.0418

11

0.1244

0.0720

11

3.5890

0.7427

11

3.1900

0.3284

0.3196

195616/68

0.0064

0.0059

11

0.0038

0.0299

0.0435

11

0.2655

0.1651

11

2.6020

1.6560

11

1.5260

0.2958

0.2965

1935140

0.0016

0.0124

11

0.0015

0.0594

0.1181

11

0.1935

10.101

31

10.2278

0.8809

11

0.2168

0.2371

0.2895

1941145

0.0071

0.0210

11

0.0069

0.0311

0.0657

11

0.1830

0.1490

11

1.7700

2.4770

11

1.7180

0.3624

0.2811

1946150

0.0047

0.0033

11

0.0040

0.0309

0.0483

11

0.1967

0.0346

11

1.1690

0.5229

11

1.0020

0.4101

0.3265

1951155

0.0122

0.0024

11

0.0110

0.0189

0.0346

11

10.037

90.0953

11

5.0210

0.5401

11

4.5050

0.2466

0.2930

1956160

0.0149

10.005

91

10.0128

0.0201

0.0333

11

0.1432

0.1955

11

5.7530

11.370

01

14.9180

0.2210

0.3130

196116/68

0.0007

0.0137

11

10.002

30.0339

0.0477

11

0.2205

0.1009

11

0.1853

2.7300

11

10.635

40.3456

0.2756

7/196812010

0.0081

0.0036

11

0.0036

0.0361

0.0594

11

0.0737

0.1976

11

5.0850

1.3660

11

2.2590

0.3260

0.2861

1970180

0.0031

0.0093

11

10.002

40.0376

0.0664

11

0.1828

0.1833

11

0.9349

1.6170

11

10.737

30.3167

0.2829

1980190

0.0181

10.005

11

10.0111

0.0391

0.0581

11

10.020

30.2402

11

5.3340

11.003

01

13.2670

0.3021

0.2873

1990100

0.0093

0.0023

11

0.0052

0.0384

0.0563

11

0.0819

0.2380

11

2.7700

0.4599

11

1.5570

0.3148

0.2767

2000110

0.0063

0.0044

11

0.0042

0.0317

0.0605

11

0.0046

0.1622

11

2.2790

0.8333

11

1.5370

0.3764

0.3019

1970175

0.0052

0.0003

11

0.0004

0.0410

0.0660

11

0.1769

0.1374

11

1.0750

0.0373

11

0.0840

0.3097

0.2774

1975180

0.0030

0.0217

11

10.003

00.0357

0.0676

11

0.1726

0.2406

11

0.7100

2.7190

11

10.729

30.3126

0.2900

1980185

0.0174

0.0001

11

0.0091

0.0365

0.0551

11

0.1018

0.2006

11

4.0440

0.0123

11

2.1130

0.3452

0.2898

1985190

0.0199

10.009

41

10.0143

0.0402

0.0588

11

10.105

00.2616

11

4.2090

11.355

01

13.0330

0.2501

0.2768

1990195

0.0077

0.0035

11

0.0037

0.0395

0.0584

11

0.1317

0.3411

11

1.6560

0.5082

11

0.8074

0.2831

0.2682

1995100

0.0133

0.0003

11

0.0091

0.0359

0.0518

11

0.0483

0.1021

11

3.1480

0.0427

11

2.1490

0.3512

0.2821

2000105

0.0085

0.0033

11

0.0062

0.0345

0.0543

11

10.097

110.004

91

12.0820

0.5126

11

1.5360

0.3327

0.3018

2005110

0.0035

0.0056

11

0.0016

0.0264

0.0628

11

0.1789

0.2699

11

1.1410

0.7522

11

0.5178

0.4088

0.3008

193512010

0.0073

0.0057

11

0.0042

0.0360

0.0624

11

0.1318

0.1082

11

6.1130

2.7580

11

3.5160

0.3168

0.2930

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!B:

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

193516/68

0.0054

0.0124

10.002

81

0.0041

0.0518

0.1208

0.0512

10.0038

0.0347

0.0002

12.1050

2.0490

11.102

01

1.5970

0.2998

0.2861

1935145

0.0106

0.0062

0.0030

10.0105

0.0622

0.1494

0.0662

10.0105

10.084

40.0001

11.9530

0.4787

0.5120

11.9270

0.2895

0.2840

1946155

0.0036

0.0132

10.004

81

0.0026

0.0316

0.0872

0.0317

10.0764

10.018

810.000

11

1.2320

1.6630

11.639

01

0.9041

0.3474

0.3007

195616/68

0.0024

0.0170

10.006

31

10.000

20.0546

0.1165

0.0485

10.2876

0.2330

0.0005

10.5456

1.7860

11.593

01

10.038

70.2707

0.2726

1935140

0.0076

0.0035

0.0025

10.0075

0.0712

0.1878

0.0707

10.1660

10.099

610.000

31

0.8962

0.1586

0.2922

10.8870

0.2428

0.2811

1941145

0.0142

0.0095

0.0036

10.0140

0.0499

0.0854

0.0610

10.1620

0.0022

0.0005

12.2060

0.8575

0.4524

12.1750

0.3448

0.2797

1946150

0.0026

0.0075

10.001

81

0.0020

0.0355

0.0954

0.0313

10.1653

10.007

510.000

11

0.5757

0.6109

10.453

81

0.4302

0.4079

0.3131

1951155

0.0045

0.0190

10.007

71

0.0032

0.0274

0.0785

0.0322

110.085

310.106

910.000

11

1.2630

1.8690

11.845

01

0.9161

0.2869

0.2773

1956160

0.0128

10.001

310.002

01

0.0106

0.0274

0.0665

0.0271

10.2653

0.1521

0.0002

13.6070

10.154

410.578

41

3.0030

0.2376

0.2791

196116/68

10.004

40.0292

10.009

21

10.007

40.0662

0.1394

0.0586

10.2660

0.2318

0.0007

110.636

81.9880

11.485

01

11.058

00.2928

0.2675

7/196812010

0.0070

0.0073

10.002

11

0.0025

0.0641

0.1497

0.0674

10.0538

0.0293

10.000

11

2.4800

1.0950

10.707

81

0.8815

0.3226

0.2812

1970180

0.0069

0.0005

0.0044

10.0014

0.0902

0.2032

0.0949

10.0289

10.043

810.000

91

0.8734

0.0305

0.5310

10.1780

0.3330

0.2737

1980190

0.0086

0.0182

10.011

81

0.0016

0.0748

0.1754

0.0678

10.0877

0.1517

0.0005

11.3220

1.1890

11.996

01

0.2410

0.3334

0.2929

1990100

0.0114

10.005

50.0051

10.0073

0.0462

0.1165

0.0570

10.2264

0.1768

0.0004

12.8320

10.540

01.0320

11.8220

0.3160

0.2694

2000110

0.0072

0.0075

10.003

31

0.0052

0.0350

0.0969

0.0436

10.1155

10.045

610.000

21

2.3740

0.8910

10.882

91

1.6940

0.3194

0.2963

1970175

0.0033

0.0029

10.000

61

10.001

50.0896

0.1921

0.0983

110.032

110.129

910.001

41

0.3146

0.1278

10.055

31

10.138

70.3007

0.2615

1975180

0.0119

0.0027

0.0087

10.0059

0.0984

0.2229

0.1019

10.0559

0.0041

10.000

61

1.0270

0.1021

0.7237

10.5103

0.3681

0.2831

1980185

0.0108

0.0164

10.008

41

0.0024

0.0757

0.1658

0.0624

10.1315

0.1786

0.0005

11.2070

0.8393

11.141

01

0.2765

0.3668

0.2869

1985190

0.0077

0.0208

10.015

51

0.0021

0.0720

0.1791

0.0709

10.0140

0.1031

0.0003

10.9099

0.9873

11.851

01

0.2460

0.2891

0.2997

1990195

0.0122

10.009

60.0079

10.0082

0.0507

0.1214

0.0629

10.3341

0.2788

0.0010

12.0460

10.671

51.0660

11.3860

0.2946

0.2658

1995100

0.0112

0.0032

10.000

31

0.0070

0.0401

0.1080

0.0470

10.0380

0.0291

10.000

21

2.3780

0.2504

10.062

41

1.4760

0.3566

0.2676

2000105

0.0084

0.0093

10.004

91

0.0062

0.0331

0.0881

0.0497

10.0917

10.147

410.000

41

2.1670

0.8971

10.843

11

1.5880

0.2876

0.2704

2005110

0.0052

0.0067

10.002

21

0.0032

0.0364

0.0998

0.0332

10.1432

0.0273

0.0000

11.2100

0.5687

10.574

41

0.7547

0.3302

0.3113

193512010

0.0063

0.0095

10.002

41

0.0032

0.0589

0.1377

0.0608

10.1060

0.0312

0.0000

13.2430

2.0840

11.203

01

1.6490

0.3125

0.2834

TABLE!3a:!Equ

al1W

eighted!NYSE!Market!P

ortfolio!!!!!!!!!+!!!!!!!20!Single1Sort!Test!P

ortfolios!B

uilt!Usin

g!Equal1W

eighted!Securities

SUMMAR

Y!RE

SULTS!FO

R!TH

E!RE

GRESSION

Statistics

¯ �0

¯ � 1¯ �2

¯ � 3�0�

Rf

s(�0)

s(�

1)

s(�2)

s(�3)

⇢ 0(�

0�R

f)⇢

M(�

1)

⇢0(�

2)

⇢0(�3)

t(¯ �0)

t(¯ �1)

t(¯ �2)

t(¯ �3)

t(�0�

Rf)

r2s(

r2)

Rp

=�0t+

�1t�

p+�2t�

2 p+�3ts p

(ei)

+⌘

p

15

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Perio

d!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!C:

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

193516/68

0.0091

0.0072

110.017

80.0078

0.0431

0.0739

10.7547

0.0076

10.068

91

0.0159

4.2300

1.9630

110.472

63.6180

0.2914

0.2866

1935145

0.0103

0.0137

110.038

40.0102

0.0566

0.1070

10.6163

0.0101

10.150

01

10.004

82.0890

1.4650

110.712

72.0600

0.2828

0.2772

1946155

0.0102

0.0064

110.077

00.0093

0.0344

0.0535

10.6997

10.020

00.0238

110.055

43.2540

1.3110

111.205

02.9550

0.3403

0.3104

195616/68

0.0071

0.0023

10.0475

0.0045

0.0352

0.0482

10.8939

0.2411

0.1623

10.0934

2.4840

0.5797

10.6507

1.5720

0.2598

0.2710

1935140

0.0091

0.0102

110.064

60.0090

0.0688

0.1361

10.5118

0.0604

10.175

31

10.012

31.1160

0.6314

111.063

01.1060

0.2375

0.2797

1941145

0.0118

0.0178

110.007

40.0116

0.0379

0.0565

10.7242

0.0896

0.0273

10.0179

2.4060

2.4450

110.078

72.3610

0.3364

0.2667

1946150

0.0071

0.0073

110.089

90.0064

0.0406

0.0619

10.7454

0.0494

0.0319

110.029

41.3490

0.9186

110.934

01.2220

0.4080

0.3061

1951155

0.0134

0.0055

110.064

10.0121

0.0268

0.0441

10.6569

10.134

310.099

91

10.080

43.8680

0.9614

110.755

83.5100

0.2725

0.3021

1956160

0.0116

10.008

51

0.1002

0.0095

0.0312

0.0356

10.9775

0.2965

0.0921

10.2156

2.8740

11.855

01

0.7938

2.3530

0.2233

0.2784

196116/68

0.0042

0.0095

10.0124

0.0012

0.0374

0.0541

10.8374

0.1884

0.1497

10.0148

1.0550

1.6640

10.1401

0.3098

0.2842

0.2647

7/196812010

0.0088

0.0035

110.006

60.0042

0.0436

0.0808

11.0760

0.0063

0.0295

110.091

84.5390

0.9742

110.138

52.1940

0.2960

0.2764

1970180

10.000

10.0032

10.1222

10.005

60.0473

0.0762

11.1730

0.1540

0.0554

10.0543

10.025

00.4763

11.1970

11.356

00.2955

0.2734

1980190

0.0204

0.0026

110.122

00.0133

0.0436

0.1012

11.1440

10.016

70.0230

110.183

15.3720

0.2932

111.225

03.5200

0.2983

0.2828

1990100

0.0052

10.003

21

0.1190

0.0011

0.0396

0.0675

10.7778

10.023

40.2170

10.0722

1.5070

10.553

21

1.7570

0.3224

0.3015

0.2708

2000110

0.0102

0.0027

110.026

60.0081

0.0478

0.0823

11.2600

10.181

810.052

91

10.288

92.4480

0.3835

110.242

51.9490

0.3064

0.2862

1970175

0.0000

10.004

51

0.1419

10.004

80.0523

0.0777

11.2710

0.1183

0.0467

10.0544

0.0002

10.492

31

0.9472

10.777

60.2837

0.2630

1975180

0.0022

0.0146

10.0931

10.003

80.0445

0.0743

11.1790

0.2655

0.0039

10.1681

0.4125

1.6680

10.6701

10.738

50.3029

0.2871

1980185

0.0194

0.0009

110.037

30.0111

0.0442

0.0828

11.1700

0.0896

10.005

91

10.219

13.7290

0.0962

110.270

72.1380

0.3171

0.2801

1985190

0.0230

0.0039

110.200

30.0173

0.0416

0.1157

11.1020

10.112

50.0311

110.160

34.6870

0.2894

111.542

03.5480

0.2632

0.2854

1990195

0.0065

0.0002

10.0574

0.0025

0.0349

0.0694

10.6334

0.0448

0.3214

10.0899

1.5730

0.0268

10.7685

0.6096

0.2803

0.2671

1995100

0.0061

10.007

71

0.1863

0.0019

0.0418

0.0632

10.8563

10.052

40.0748

10.0479

1.2470

11.036

01

1.8460

0.3818

0.3323

0.2684

2000105

0.0104

10.002

41

0.0507

0.0081

0.0477

0.0629

11.1130

10.328

910.091

91

10.300

51.8470

10.327

31

0.3862

1.4430

0.2728

0.2723

2005110

0.0106

0.0102

110.145

60.0087

0.0457

0.0946

11.3570

10.054

210.050

31

10.289

91.9730

0.9146

110.910

81.6120

0.3172

0.2946

193512010

0.0089

0.0051

110.011

50.0058

0.0433

0.0778

10.9478

0.0469

10.008

51

10.044

76.2050

1.9940

110.367

44.0360

0.2940

0.2808

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!D:

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

193516/68

0.0069

0.0115

10.001

710.007

90.0056

0.0663

0.1198

0.0586

0.8325

0.0053

0.0456

0.0001

10.022

22.0940

1.9250

10.584

510.189

01.6960

0.3049

0.2929

1935145

0.0159

0.0061

0.0059

10.083

00.0158

0.0848

0.1454

0.0814

0.7943

0.0157

10.068

110.000

110.054

92.1460

0.4840

0.8296

11.195

02.1270

0.2907

0.2902

1946155

0.0054

0.0135

10.004

010.037

10.0045

0.0408

0.0869

0.0317

0.6697

10.123

210.006

910.000

110.065

51.4620

1.6990

11.369

010.606

21.2070

0.3542

0.3093

195616/68

0.0003

0.0146

10.006

60.0811

10.002

30.0638

0.1184

0.0506

0.9686

0.1787

0.2218

0.0004

0.0466

0.0552

1.5140

11.586

01.0250

10.444

60.2778

0.2784

1935140

0.0134

0.0026

0.0058

10.087

30.0133

0.0904

0.1815

0.0864

0.8029

0.0212

10.078

510.000

810.065

41.2470

0.1212

0.5626

10.916

41.2400

0.2383

0.2881

1941145

0.0189

0.0103

0.0061

10.077

80.0186

0.0782

0.0864

0.0758

0.7908

0.0705

10.019

80.0007

10.019

21.8680

0.9268

0.6189

10.761

81.8470

0.3527

0.2827

1946150

0.0070

0.0077

0.0001

10.090

70.0063

0.0488

0.0961

0.0328

0.7075

10.079

90.0125

10.000

110.046

71.1100

0.6201

0.0214

10.993

21.0030

0.4133

0.3119

1951155

0.0039

0.0193

10.008

00.0166

0.0027

0.0312

0.0769

0.0304

0.6311

10.165

310.110

910.000

110.070

50.9689

1.9390

12.041

00.2036

0.6643

0.2951

0.2975

1956160

0.0080

10.005

710.002

50.1631

0.0059

0.0482

0.0660

0.0327

1.1190

0.0869

0.1753

0.0001

0.1210

1.2930

10.673

810.587

01.1290

0.9553

0.2490

0.2791

196116/68

10.004

90.0282

10.009

30.0264

10.007

80.0722

0.1419

0.0597

0.8559

0.1909

0.2127

0.0006

10.000

810.641

31.8880

11.474

00.2927

11.027

00.2971

0.2778

7/196812010

0.0057

0.0067

10.002

60.0321

0.0012

0.0732

0.1534

0.0701

0.9905

0.0516

0.0180

0.0000

10.046

41.7570

0.9844

10.851

60.7310

0.3581

0.3303

0.2844

1970180

10.000

910.000

80.0005

0.1753

10.006

40.1021

0.1961

0.0954

1.0320

0.0971

10.052

210.000

50.1679

10.106

510.044

90.0570

1.9520

10.721

80.3369

0.2755

1980190

0.0085

0.0199

10.012

910.005

20.0014

0.0768

0.1803

0.0660

0.9907

0.0988

0.1593

0.0008

10.178

11.2690

1.2700

12.241

010.060

60.2159

0.3360

0.2936

1990100

0.0092

10.010

40.0062

0.0767

0.0051

0.0554

0.1204

0.0658

0.8139

0.1407

0.0863

0.0003

0.0806

1.9000

10.989

91.0880

1.0820

1.0530

0.3239

0.2814

2000110

0.0075

0.0092

10.004

110.014

20.0054

0.0478

0.1093

0.0407

1.1280

10.060

310.097

210.000

110.217

51.7970

0.9696

11.154

010.144

91.2940

0.3343

0.2984

1970175

10.009

40.0092

10.009

00.2177

10.014

20.1054

0.1903

0.0997

1.1340

0.0748

10.131

810.000

80.3115

10.759

90.4114

10.764

91.6290

11.145

00.3116

0.2580

1975180

0.0106

10.006

80.0102

0.1043

0.0046

0.1045

0.2129

0.1003

0.9444

0.0788

10.008

010.000

70.1161

0.8634

10.272

00.8652

0.9374

0.3764

0.3649

0.2904

1980185

0.0114

0.0155

10.007

810.005

70.0030

0.0756

0.1804

0.0612

1.0540

0.1147

0.1812

0.0006

10.222

31.2750

0.7290

11.083

010.045

70.3438

0.3670

0.2899

1985190

0.0068

0.0248

10.018

10.0000

0.0011

0.0754

0.1767

0.0682

0.9093

0.0743

0.0985

0.0009

10.128

20.7622

1.1920

12.249

00.0003

0.1281

0.2934

0.3001

1990195

0.0161

10.014

00.0137

10.070

70.0121

0.0606

0.1250

0.0786

0.7700

0.1205

0.1753

0.0006

0.0441

2.2530

10.948

71.4840

10.778

71.6970

0.3036

0.2801

1995100

0.0019

10.002

310.004

80.2471

10.002

40.0453

0.1121

0.0431

0.7783

0.1132

10.026

110.000

10.1115

0.3555

10.177

710.943

02.6940

10.445

00.3616

0.2759

2000105

0.0049

0.0081

10.007

20.0971

0.0026

0.0504

0.0936

0.0459

1.0620

10.158

210.164

710.000

110.210

60.8179

0.7340

11.328

00.7753

0.4355

0.3051

0.2761

2005110

0.0102

0.0125

10.001

210.154

70.0083

0.0452

0.1175

0.0320

1.1800

10.042

610.046

80.0000

10.300

61.9150

0.8992

10.305

511.112

01.5450

0.3429

0.3111

193512010

0.0062

0.0088

10.002

20.0145

0.0031

0.0702

0.1395

0.0653

0.9240

0.0635

0.0272

0.0001

10.035

62.6820

1.9060

11.033

00.4734

1.3420

0.3191

0.2882

TABLE!3a:!Equ

al1W



ortfolios!B

uilt!Usin

g!Equal1W

eighted!Securities

SUMMAR

Y!RE

SULTS!FO

R!TH

E!RE

GRESSION!(con

t.)

Statistics

¯ �0

¯ � 1¯ �2

¯ � 3�0�

Rf

s(�0)

s(�

1)

s(�2)

s(�3)

⇢ 0(�

0�R

f)⇢

M(�

1)

⇢0(�

2)

⇢0(�3)

t(¯ �0)

t(¯ �1)

t(¯ �2)

t(¯ �3)

t(�0�

Rf)

r2s(

r2)

Rp

=�0t+

�1t�

p+�2t�

2 p+�3ts p

(ei)

+⌘

p

16

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Perio

d!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!A:

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

193516/68

0.0060

0.0086

11

0.0047

0.0356

0.0661

11

0.0045

0.0378

11

3.3930

2.6110

11

2.6530

0.2589

0.2666

1935145

0.0040

0.0165

11

0.0038

0.0466

0.0979

11

0.0038

10.013

21

10.9717

1.9310

11

0.9368

0.2677

0.2522

1946155

0.0090

0.0022

11

0.0081

0.0258

0.0392

11

0.0341

0.0758

11

3.8340

0.6220

11

3.4360

0.2654

0.2938

195616/68

0.0054

0.0068

11

0.0028

0.0310

0.0453

11

0.2620

0.1762

11

2.1460

1.8510

11

1.1080

0.2461

0.2572

1935140

0.0020

0.0119

11

0.0020

0.0566

0.1189

11

0.0533

10.056

31

10.3024

0.8452

11

0.2909

0.2276

0.2504

1941145

0.0062

0.0219

11

0.0060

0.0311

0.0654

11

0.1873

0.1390

11

1.5510

2.5960

11

1.4980

0.3152

0.2480

1946150

0.0058

0.0021

11

0.0051

0.0303

0.0441

11

0.1109

0.0334

11

1.4830

0.3642

11

1.3140

0.3477

0.3030

1951155

0.0123

0.0024

11

0.0110

0.0201

0.0339

11

10.102

40.1101

11

4.7290

0.5425

11

4.2470

0.1831

0.2616

1956160

0.0137

10.004

71

10.0116

0.0217

0.0344

11

0.1391

0.1421

11

4.8830

11.061

01

14.1200

0.1831

0.2646

196116/68

10.000

10.0145

11

10.003

00.0349

0.0499

11

0.2273

0.1426

11

10.025

02.7640

11

10.821

40.2881

0.2447

7/196812010

0.0081

0.0036

11

0.0036

0.0358

0.0583

11

0.0810

0.2038

11

5.1250

1.3980

11

2.2750

0.2830

0.2581

1970180

0.0031

0.0093

11

10.002

40.0395

0.0663

11

0.1371

0.2102

11

0.9007

1.6180

11

10.689

80.2972

0.2660

1980190

0.0172

10.004

11

10.0102

0.0385

0.0587

11

0.0139

0.2295

11

5.1380

10.799

41

13.0460

0.2616

0.2593

1990100

0.0098

0.0017

11

0.0057

0.0372

0.0537

11

0.1143

0.2472

11

3.0170

0.3619

11

1.7650

0.2515

0.2374

2000110

0.0058

0.0049

11

0.0037

0.0308

0.0578

11

0.0457

0.1592

11

2.1630

0.9819

11

1.3980

0.3021

0.2628

1970175

0.0062

10.000

81

10.0015

0.0443

0.0657

11

0.1101

0.1788

11

1.1970

10.103

11

10.2773

0.3149

0.2661

1975180

0.0023

0.0224

11

10.003

70.0366

0.0663

11

0.1530

0.2594

11

0.5427

2.8630

11

10.861

80.2734

0.2636

1980185

0.0179

10.000

41

10.0095

0.0350

0.0552

11

0.1287

0.1835

11

4.3340

10.062

81

12.3230

0.3060

0.2561

1985190

0.0183

10.007

61

10.0126

0.0409

0.0598

11

10.052

60.2593

11

3.7960

11.084

01

12.6390

0.2238

0.2602

1990195

0.0084

0.0028

11

0.0044

0.0377

0.0547

11

0.1664

0.3471

11

1.8860

0.4344

11

0.9971

0.2366

0.2303

1995100

0.0136

0.0000

11

0.0093

0.0355

0.0508

11

0.0861

0.1332

11

3.2430

10.006

91

12.2320

0.2730

0.2561

2000105

0.0079

0.0040

11

0.0056

0.0323

0.0513

11

10.057

10.0337

11

2.0640

0.6612

11

1.4810

0.2645

0.2517

2005110

0.0031

0.0060

11

0.0011

0.0270

0.0607

11

0.1823

0.2286

11

0.9688

0.8427

11

0.3598

0.3307

0.2694

193512010

0.0072

0.0058

11

0.0041

0.0357

0.0619

11

0.1041

0.1238

11

6.0890

2.8360

11

3.4650

0.2724

0.2620

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!B:

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

193516/68

0.0085

0.0032

0.0025

10.0072

0.0499

0.1068

0.0516

10.0068

10.100

510.000

31

3.4230

0.5930

0.9614

12.9000

0.2610

0.2623

1935145

0.0112

0.0006

0.0072

10.0110

0.0597

0.1186

0.0653

10.0112

10.281

010.000

81

2.1440

0.0554

1.2620

12.1170

0.2407

0.2478

1946155

0.0028

0.0153

10.005

81

0.0018

0.0333

0.0955

0.0352

10.0204

10.030

210.000

11

0.9136

1.7490

11.819

01

0.6022

0.3046

0.2889

195616/68

0.0108

10.004

20.0050

10.0082

0.0515

0.1043

0.0485

10.0845

0.0479

0.0001

12.5730

10.497

91.2630

11.9530

0.2439

0.2497

1935140

0.0085

10.002

20.0066

10.0084

0.0701

0.1460

0.0763

110.091

010.283

410.001

61

1.0220

10.128

80.7257

11.0120

0.2010

0.2515

1941145

0.0143

0.0039

0.0079

10.0141

0.0446

0.0755

0.0499

10.1625

10.267

20.0001

12.4890

0.3996

1.2340

12.4530

0.2877

0.2368

1946150

0.0031

0.0071

10.001

91

0.0024

0.0333

0.0930

0.0288

10.1562

10.016

410.000

11

0.7169

0.5888

10.498

41

0.5612

0.3849

0.2896

1951155

0.0025

0.0234

10.009

81

0.0012

0.0336

0.0980

0.0405

110.158

210.110

510.000

11

0.5705

1.8520

11.883

01

0.2881

0.2243

0.2671

1956160

0.0138

10.005

10.0003

10.0117

0.0339

0.0833

0.0338

10.1939

0.0802

0.0002

13.1560

10.470

60.0575

12.6700

0.2075

0.2530

196116/68

0.0088

10.003

70.0082

10.0059

0.0606

0.1167

0.0562

10.0565

0.0344

0.0001

11.3840

10.300

41.3800

10.9242

0.2682

0.2458

7/196812010

0.0064

0.0096

10.003

51

0.0018

0.0593

0.1391

0.0623

10.0678

0.0152

10.000

21

2.4290

1.5630

11.270

01

0.7051

0.2887

0.2440

1970180

0.0047

0.0065

0.0011

110.000

80.0842

0.1824

0.0801

10.0722

10.016

110.000

51

0.6417

0.4091

0.1543

110.103

70.3023

0.2450

1980190

0.0118

0.0111

10.008

41

0.0048

0.0721

0.1618

0.0655

10.0386

0.0633

10.000

11

1.8830

0.7852

11.471

01

0.7655

0.2952

0.2489

1990100

0.0070

0.0097

10.004

11

0.0029

0.0448

0.1194

0.0625

10.0999

0.0088

10.000

11

1.7910

0.9345

10.756

31

0.7447

0.2720

0.2306

2000110

0.0058

0.0088

10.003

01

0.0038

0.0357

0.1147

0.0524

10.1117

0.0228

10.000

31

1.8780

0.8785

10.666

21

1.2150

0.2859

0.2477

1970175

0.0009

0.0116

10.006

21

10.003

90.0830

0.1709

0.0829

10.1053

10.029

910.000

41

0.0898

0.5780

10.634

71

10.399

30.3019

0.2438

1975180

0.0122

0.0009

0.0100

10.0062

0.0927

0.2003

0.0859

10.0302

10.013

010.000

71

1.1200

0.0390

0.9909

10.5719

0.3029

0.2476

1980185

0.0162

0.0035

10.001

91

0.0079

0.0806

0.1722

0.0687

10.0400

0.0929

10.000

11

1.7090

0.1733

10.238

91

0.8385

0.3344

0.2418

1985190

0.0096

0.0171

10.013

81

0.0040

0.0595

0.1434

0.0586

110.004

510.020

210.000

31

1.3690

1.0100

11.998

01

0.5664

0.2591

0.2491

1990195

0.0070

0.0074

10.002

51

0.0030

0.0461

0.1215

0.0668

10.1667

0.0022

10.000

11

1.2860

0.5178

10.316

91

0.5538

0.2340

0.2106

1995100

0.0086

0.0138

10.006

91

0.0043

0.0425

0.1117

0.0535

10.0144

0.0093

0.0000

11.7110

1.0460

11.091

01

0.8613

0.3209

0.2411

2000105

0.0083

0.0055

10.001

51

0.0060

0.0351

0.1018

0.0591

10.0685

10.165

710.000

71

2.0030

0.4574

10.215

31

1.4650

0.2790

0.2323

2005110

0.0021

0.0144

10.005

81

0.0001

0.0358

0.1209

0.0410

10.1425

0.1446

0.0002

10.4953

1.0070

11.197

01

0.0343

0.2799

0.2595

193512010

0.0073

0.0068

10.000

91

0.0042

0.0554

0.1259

0.0579

10.0542

10.021

210.000

21

3.9950

1.6260

10.454

21

2.3000

0.2765

0.2525

TABLE!3e:!Equ

al1W


ortfolio!!!!!!!!!+!!!!!!!5x5!Do

uble1Sort!T

est!P

ortfolios!B

uilt!Usin

g!Eq

ual1W

eighted!Securities

SUMMAR

Y!RE

SULTS!FO

R!TH

E!RE

GRESSION

Statistics

¯ �0

¯ � 1¯ �2

¯ � 3�0�

Rf

s(�0)

s(�

1)

s(�2)

s(�3)

⇢ 0(�

0�R

f)⇢

M(�

1)

⇢0(�

2)

⇢0(�3)

t(¯ �0)

t(¯ �1)

t(¯ �2)

t(¯ �3)

t(�0�

Rf)

r2s(

r2)

Rp

=�0t+

�1t�

p+�2t�

2 p+

�3ts p

(ei)

+⌘

p

17

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Perio

d!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!C:

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

193516/68

0.0050

0.0016

10.0866

0.0037

0.0384

0.0606

10.6482

0.0034

10.090

11

0.0684

2.5980

0.5196

12.6760

1.9140

0.3175

0.2612

1935145

0.0018

0.0000

10.1641

0.0016

0.0492

0.0841

10.5208

0.0016

10.170

41

0.0454

0.4140

10.005

21

3.6070

0.3807

0.3000

0.2470

1946155

0.0103

0.0062

110.081

20.0094

0.0290

0.0492

10.4861

10.049

710.021

81

10.028

83.8960

1.3850

111.831

03.5430

0.3405

0.2855

195616/68

0.0035

10.000

71

0.1532

0.0009

0.0338

0.0415

10.8185

0.2586

0.1145

10.1666

1.2700

10.218

31

2.2930

0.3242

0.3144

0.2534

1935140

0.0021

10.002

11

0.0949

0.0021

0.0584

0.1054

10.5287

0.0060

10.179

31

10.001

20.3089

10.167

61

1.5120

0.2978

0.2775

0.2457

1941145

0.0014

0.0024

10.2461

0.0011

0.0358

0.0487

10.5034

0.1998

10.124

81

0.1019

0.2921

0.3814

13.7870

0.2444

0.3266

0.2478

1946150

0.0060

0.0042

110.032

60.0053

0.0319

0.0574

10.4778

0.0113

10.036

91

10.050

11.4580

0.5715

110.528

61.2970

0.4180

0.2793

1951155

0.0147

0.0082

110.129

90.0134

0.0254

0.0397

10.4936

10.136

010.103

91

10.006

44.4670

1.5990

112.038

04.0870

0.2631

0.2723

1956160

0.0130

10.005

91

0.0322

0.0109

0.0247

0.0371

10.5821

0.0626

0.1359

10.0319

4.0760

11.232

01

0.4290

3.4080

0.2538

0.2500

196116/68

10.002

80.0027

10.2339

10.005

80.0376

0.0441

10.9384

0.2378

0.0876

10.2569

10.710

40.5806

12.3640

11.446

00.3548

0.2488

7/196812010

0.0079

0.0009

10.0324

0.0034

0.0418

0.0598

10.9183

0.0859

0.0031

10.0840

4.2780

0.3229

10.7958

1.8370

0.3312

0.2532

1970180

0.0005

10.000

81

0.1443

10.004

90.0489

0.0605

11.2250

0.1954

10.033

41

0.2706

0.1228

10.152

91

1.3540

11.161

00.3380

0.2645

1980190

0.0190

0.0013

110.088

50.0120

0.0431

0.0688

10.8337

0.0163

10.009

61

10.026

15.0660

0.2168

111.220

03.1970

0.3062

0.2512

1990100

0.0104

0.0030

110.021

70.0063

0.0419

0.0590

10.7722

0.0728

10.018

81

0.0234

2.8560

0.5784

110.323

41.7450

0.3393

0.2469

2000110

0.0044

10.005

91

0.1501

0.0023

0.0368

0.0582

10.8075

0.0020

0.0422

10.0445

1.3680

11.165

01

2.1360

0.7276

0.3484

0.2438

1970175

0.0082

0.0052

110.099

10.0034

0.0556

0.0650

11.4120

0.0976

10.128

01

0.1974

1.2530

0.6777

110.595

90.5216

0.3346

0.2576

1975180

10.004

510.003

21

0.3783

10.010

50.0426

0.0583

10.9849

0.2945

0.0334

10.3425

10.901

410.461

01

3.2590

12.114

00.3401

0.2732

1980185

0.0180

10.000

21

10.004

20.0096

0.0400

0.0618

10.8951

0.1859

10.107

91

0.0262

3.8090

10.030

71

10.039

82.0590

0.3565

0.2556

1985190

0.0212

0.0019

110.153

60.0156

0.0449

0.0726

10.7251

10.095

10.0532

110.078

84.0090

0.2221

111.797

02.9530

0.2501

0.2304

1990195

0.0080

10.001

01

0.0514

0.0040

0.0407

0.0499

10.6570

0.1199

10.033

81

0.0079

1.6630

10.168

41

0.6641

0.8395

0.2738

0.2274

1995100

0.0154

0.0069

110.104

10.0112

0.0413

0.0647

10.8246

0.0535

10.017

81

0.0397

3.1680

0.9118

111.071

02.2990

0.4046

0.2482

2000105

0.0051

10.008

61

0.1887

0.0028

0.0394

0.0545

10.8425

10.112

710.094

21

0.0222

1.1000

11.336

01

1.9010

0.6179

0.3605

0.2374

2005110

0.0029

10.004

51

0.1295

0.0009

0.0316

0.0591

10.7624

0.1721

0.1640

10.0675

0.7666

10.639

21

1.4410

0.2464

0.3407

0.2515

193512010

0.0066

0.0012

10.0562

0.0035

0.0404

0.0601

10.8106

0.0948

10.038

01

0.0769

4.9570

0.5878

12.0940

2.6360

0.3252

0.2567

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!D:

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

193516/68

0.0011

0.0086

10.004

00.1056

10.000

20.0562

0.1066

0.0520

0.6859

10.000

60.0120

0.0002

0.1020

0.4063

1.6090

11.525

03.0820

10.058

50.3321

0.2652

1935145

10.005

80.0152

10.008

90.1914

10.005

90.0621

0.1207

0.0685

0.5598

10.005

710.083

30.0002

0.0638

11.060

01.4400

11.485

03.9140

11.087

00.3099

0.2472

1946155

0.0061

0.0132

10.003

610.059

70.0051

0.0326

0.0892

0.0297

0.4663

0.0189

0.0192

0.0000

10.014

02.0370

1.6200

11.335

011.401

01.7190

0.3628

0.2853

195616/68

0.0032

10.000

90.0001

0.1627

0.0006

0.0648

0.1064

0.0493

0.8855

0.2237

0.1108

0.0003

0.2280

0.6093

10.104

60.0165

2.2510

0.1166

0.3268

0.2631

1935140

10.005

90.0157

10.010

70.1162

10.006

00.0725

0.1476

0.0831

0.6006

0.0897

10.033

70.0006

0.0221

10.685

30.8979

11.081

01.6300

10.694

30.2863

0.2495

1941145

10.005

60.0145

10.006

80.2804

10.005

80.0476

0.0790

0.0460

0.4976

0.0375

10.285

210.000

20.1137

10.909

31.4250

11.140

04.3650

10.946

00.3379

0.2436

1946150

0.0038

0.0068

10.001

410.012

60.0031

0.0342

0.0878

0.0257

0.4863

0.0404

0.0543

0.0000

10.030

30.8570

0.6042

10.434

610.200

60.7047

0.4462

0.2656

1951155

0.0083

0.0195

10.005

810.106

70.0071

0.0311

0.0908

0.0333

0.4446

10.070

410.085

80.0000

0.0032

2.0810

1.6650

11.348

011.859

01.7760

0.2795

0.2820

1956160

0.0126

10.005

610.000

20.0378

0.0105

0.0340

0.0827

0.0296

0.5476

10.147

40.0508

0.0000

0.0083

2.8740

10.522

210.043

90.5340

2.3930

0.2644

0.2609

196116/68

10.003

00.0022

0.0002

0.2461

10.006

00.0786

0.1200

0.0590

1.0470

0.2536

0.1260

0.0006

0.3757

10.364

90.1742

0.0358

2.2300

10.719

00.3683

0.2577

7/196812010

0.0042

0.0085

10.005

00.0597

10.000

30.0764

0.1407

0.0665

0.9919

0.1694

0.0407

0.0003

0.1560

1.2390

1.3630

11.712

01.3590

10.102

90.3710

0.2537

1970180

10.001

10.0003

10.001

20.1671

10.006

50.1059

0.1802

0.0860

1.3090

0.2410

10.023

30.0005

0.4383

10.114

50.0207

10.156

41.4670

10.707

30.3855

0.2644

1980190

0.0130

0.0137

10.008

310.048

80.0059

0.0957

0.1683

0.0818

0.9613

0.1128

0.0467

0.0004

0.0166

1.5540

0.9378

11.161

010.583

50.7114

0.3538

0.2538

1990100

0.0047

0.0151

10.008

40.0209

0.0006

0.0660

0.1213

0.0625

0.8488

0.2237

0.1624

0.0007

0.0609

0.8161

1.4250

11.538

00.2834

0.1054

0.3634

0.2492

2000110

0.0002

0.0047

10.005

80.1644

10.001

90.0388

0.1109

0.0446

0.7715

0.0594

0.0275

10.000

20.0472

0.0474

0.4913

11.507

02.4480

10.568

80.3914

0.2455

1970175

0.0042

0.0121

10.004

210.075

510.000

50.1071

0.1719

0.0858

1.5120

0.2671

10.032

70.0009

0.4573

0.3361

0.5988

10.419

110.423

810.043

40.3745

0.2595

1975180

10.001

210.011

10.0043

0.3724

10.007

20.1088

0.1975

0.0928

1.0080

0.2075

10.043

80.0000

0.3982

10.091

910.474

50.3946

3.1350

10.561

40.3960

0.2687

1980185

0.0151

0.0044

10.002

80.0139

0.0068

0.0956

0.1693

0.0748

0.9475

0.2060

0.0325

0.0005

0.1088

1.3440

0.2213

10.316

60.1245

0.6099

0.4056

0.2480

1985190

0.0126

0.0209

10.012

810.097

90.0069

0.0921

0.1589

0.0840

0.9329

10.006

50.0311

0.0000

10.071

21.1600

1.1140

11.291

010.890

20.6416

0.2966

0.2443

1990195

10.001

80.0200

10.014

20.1160

10.005

70.0753

0.1293

0.0750

0.7968

0.2403

0.2243

0.0012

0.0455

10.199

61.3140

11.606

01.2350

10.648

10.3020

0.2337

1995100

0.0126

0.0110

10.003

210.067

30.0083

0.0518

0.1077

0.0417

0.8429

0.1727

0.0528

0.0001

0.0756

2.0640

0.8657

10.646

110.677

01.3670

0.4292

0.2471

2000105

0.0007

0.0013

10.005

40.2101

10.001

60.0373

0.0952

0.0454

0.7878

0.0708

10.198

210.000

60.0583

0.1582

0.1188

11.017

02.2630

10.360

10.3992

0.2394

2005110

10.002

40.0096

10.007

80.1408

10.004

30.0404

0.1190

0.0422

0.7598

0.0213

0.1672

0.0001

0.0387

10.493

90.6825

11.562

01.5730

10.899

70.3918

0.2497

193512010

0.0028

0.0085

10.004

60.0799

10.000

30.0682

0.1268

0.0605

0.8704

0.1637

0.0317

0.0003

0.1326

1.2600

2.0300

12.277

02.7700

10.118

20.3538

0.2594

TABLE!3e:!Equ

al1W


ortfolio!!!!!!!!!+!!!!!!!5x5!Do

uble1Sort!T

est!P

ortfolios!B

uilt!Usin

g!Eq

ual1W

eighted!Securities

SUMMAR

Y!RE

SULTS!FO

R!TH

E!RE

GRESSION!(con

t.)

Statistics

¯ �0

¯ � 1¯ �2

¯ � 3�0�

Rf

s(�0)

s(�

1)

s(�2)

s(�3)

⇢ 0(�

0�R

f)⇢

M(�

1)

⇢0(�

2)

⇢0(�3)

t(¯ �0)

t(¯ �1)

t(¯ �2)

t(¯ �3)

t(�0�

Rf)

r2s(

r2)

Rp

=�0t+

�1t�

p+�2t�

2 p+

�3ts p

(ei)

+⌘

p

18

3.3 Behavior of the market

For completeness I replicate and extend the last two tables of Fama-MacBeth (1973) anddescribe the results below. First in Table 4a we note that the average monthly return on themarket portfolio proxy (the equal-weighted NYSE portfolio) is Rm � 1.25% for 1935-2010but it is greater for the 1935-6/1968 testing period (Rm � 1.45%) than for the 7/1968-2010testing period (Rm � 1.10%). On the other hand, the return in excess of the three-monthTreasury Bill9 is halved from 1935-6/1968 to 7/1968-2010 because Rf increases from an av-erage monthly return of 13bps for 1935-6/1968 to 45bps for the 7/1968-2010 testing period.These results may not be so surprising because the post-1968 period includes several notice-able downturns (in the late 1980s, the early 2000’s and more recently in the late 2000’s).However, the equal-weighted NYSE is slightly less volatile for the 7/1968-2010 testing period(spRmq � 5.41%) than for the 1935-6/1968 period (spRmq � 6.12%); this is a bit surprisinggiven the previous observation. ¯γ0 and ¯γ1 are the estimates from the regression specificationin Panel A of Table 3a. Recall that for the Sharpe-Lintner model Epγ0tq � Rf while in theBlack model Epγ0tq is the expected return on the portfolio with zero beta with respect to themarket portfolio proxy. In both models, Epγ1tq is the excess return of the market portfolio(proxy) on γ0t. I find that ¯γ0 is fairly large10 and more volatile relative to the proxy forthe risk-free rate, Rf . Furthermore ¯γ0 is significantly less autocorrelated than Rf ; indeedρMpγ0q � 0.1361 and ρMpRf q � 0.9763 for the 1935-2010 testing period. Nonetheless, I doalso find that ¯γ1 � ¯γ0 � Rm in all testing periods.

When I use the value-weighted NYSE portfolio returns as a proxy for the market portfolioreturn I find that Rm decreases and is less volatile. Indeed, from Table 4h, Rm � 1.09%,88bps, and 97bps for the 1935-6/1968, 7/1968-2010, and 1935-2010 testing periods (respec-tively). In addition, the standard deviation of the monthly returns (spRmq) is much lowerand is (close to) 4.50% for the three aforementioned testing periods. The resulting Sharpe

ratios�Rm�Rf

spRmq

are also lower with the value-weighted NYSE portfolio returns compared to

the equal-weighted NYSE portfolio returns. In Table 4h, I also use the 5 � 5 dual-sort testportfolios where the portfolio betas are the value-weighted averages of the underlying secu-rity betas. I find that ¯γ1 tends to have much lower magnitude compared the correspondingvalues in Table 4a. More specifically, with the 5 � 5 test portfolios ¯γ1 is about half the cor-responding values if I use the 20 Fama-MacBeth (1973) test portfolios for the 1935-6/1968,7/1968-2010, and 1935-2010 testing periods. Nonetheless, I still find ¯γ1 � ¯γ0 � Rm and theautocorrelation of ¯γ0 is much lower than that of Rf (ρMpγ0q ρMpRf q). However, ρMpγ0qtends to be lower in Table 4h than in Table 4a.

9I obtain the monthly returns of the three-month Treasury Bill from the Fama-French data library10γ0 tends to be significantly larger than Rf . From Panel A of Table 3a, tpγ0 � Rf q tends to be larger

than the relevant critical values for statistical significance.

19

! ! ! ! ! ! ! ! ! ! ! !! ! !

Period

1935,6/68 0.0145 0.0132 0.0084 0.0063 0.0013 0.2154 0.1369 0.0612 0.0613 ! !

1935,45 0.0201 0.0200 0.0163 0.0041 0.0001 0.2246 0.1832 0.0890 0.0890 ! !1946,55 0.0112 0.0103 0.0028 0.0084 0.0009 0.2370 0.0653 0.0434 0.0434 ! !1956,6/68 0.0122 0.0095 0.0059 0.0064 0.0026 0.2392 0.1474 0.0399 0.0400 ! !

1935,40 0.0141 0.0141 0.0124 0.0016 0.0001 0.1292 0.1136 0.1087 0.1087 ! !1941,45 0.0273 0.0270 0.0210 0.0071 0.0002 0.4669 0.3627 0.0579 0.0578 ! !1946,50 0.0077 0.0070 0.0033 0.0047 0.0007 0.1355 0.0626 0.0520 0.0520 ! !1951,55 0.0147 0.0135 0.0024 0.0122 0.0012 0.4144 0.0739 0.0326 0.0328 ! !1956,60 0.0091 0.0070 ,0.0059 0.0149 0.0021 0.2069 ,0.1735 0.0340 0.0342 ! !1961,6/68 0.0142 0.0112 0.0137 0.0007 0.0029 0.2581 0.3158 0.0435 0.0435 ! !

7/1968,2010 0.0110 0.0065 0.0036 0.0081 0.0045 0.1193 0.0665 0.0541 0.0543 ! !

1970,80 0.0116 0.0061 0.0093 0.0031 0.0055 0.0947 0.1447 0.0646 0.0647 ! !1980,90 0.0122 0.0052 ,0.0051 0.0181 0.0071 0.098 ,0.0967 0.0525 0.0528 ! !1990,00 0.0100 0.0060 0.0023 0.0093 0.0041 0.1486 0.0562 0.0401 0.0402 ! !2000,10 0.0110 0.0089 0.0044 0.0063 0.0021 0.1560 0.0770 0.0570 0.0571 ! !

1970,75 0.0036 ,0.0012 0.0003 0.0052 0.0048 ,0.0172 0.0041 0.0702 0.0704 ! !1975,80 0.0250 0.0190 0.0217 0.0030 0.0060 0.3040 0.3463 0.0625 0.0628 ! !1980,85 0.0173 0.0089 0.0001 0.0174 0.0083 0.185 0.0016 0.0483 0.0490 ! !1985,90 0.0090 0.0034 ,0.0094 0.0199 0.0056 0.061 ,0.1714 0.0548 0.0549 ! !1990,95 0.0103 0.0063 0.0035 0.0077 0.0040 0.1616 0.0897 0.0390 0.0392 ! !1995,00 0.0113 0.0070 0.0003 0.0133 0.0043 0.181 0.0067 0.0388 0.0388 ! !2000,05 0.0127 0.0104 0.0033 0.0085 0.0023 0.2474 0.0780 0.0421 0.0422 ! !2005,10 0.0087 0.0067 0.0056 0.0035 0.0019 0.1017 0.0843 0.0661 0.0662 ! !

1935,2010 0.0125 0.0094 0.0057 0.0073 0.0031 0.1642 0.0994 0.0573 0.0575 ! !

Period

1935,6/68 0.0360 0.0012 4.7400 4.309 2.5460 3.4760 ,0.0063 ,0.0040 0.0098 0.2008 0.9661

1935,45 0.0485 0.0002 2.5890 2.5710 1.9160 0.9753 ,0.0664 ,0.0663 ,0.0470 0.1935 0.63721946,55 0.0258 0.0004 2.8350 2.597 0.7427 3.5890 0.0875 0.0864 0.0720 0.1261 0.89231956,6/68 0.0299 0.0009 3.7290 2.926 1.6560 2.6020 0.1357 0.1380 0.1651 0.2567 0.8512

1935,40 0.0594 0.0002 1.0950 1.0890 0.8809 0.2278 ,0.1260 ,0.1255 ,0.1013 0.1927 0.43611941,45 0.0311 0.0001 3.6460 3.6200 2.4770 1.7700 0.1493 0.1485 0.1490 0.1841 0.72331946,50 0.0309 0.0003 1.1480 1.0510 0.5229 1.1690 0.0922 0.0898 0.0346 0.1969 0.91021951,55 0.0189 0.0004 3.5000 3.196 0.5401 5.0210 ,0.0244 ,0.0172 0.0953 ,0.0417 0.75561956,60 0.0201 0.0007 2.0840 1.592 ,1.3700 5.7530 0.1145 0.1309 0.1955 0.1439 0.65991961,6/68 0.0339 0.0008 3.0890 2.449 2.7300 0.1853 0.1318 0.1294 0.1009 0.2153 0.8900

7/1968,2010 0.0361 0.0025 4.5880 2.685 1.3660 5.0850 0.1864 0.1905 0.1976 0.0832 0.9605

1970,80 0.0376 0.0020 2.0600 1.086 1.6170 0.9349 0.1129 0.1148 0.1833 0.1834 0.89311980,90 0.0391 0.0023 2.6750 1.124 ,1.0030 5.3340 0.1826 0.1887 0.2402 ,0.0190 0.89031990,00 0.0384 0.0011 2.8790 1.702 0.4599 2.7700 0.2137 0.2177 0.2380 0.0919 0.90552000,10 0.0317 0.0016 2.2100 1.788 0.8333 2.2790 0.2689 0.2726 0.1622 0.0165 0.9778

1970,75 0.0410 0.0013 0.4335 ,0.146 0.0373 1.0750 0.1535 0.1577 0.1374 0.1702 0.82951975,80 0.0357 0.0023 3.3950 2.570 2.7190 0.7100 0.0478 0.0543 0.2406 0.1846 0.89641980,85 0.0365 0.0022 3.0340 1.548 0.0123 4.0440 0.1518 0.1729 0.2006 0.0984 0.83061985,90 0.0402 0.0010 1.3930 0.518 ,1.3550 4.2090 0.1979 0.1980 0.2616 ,0.0928 0.77271990,95 0.0395 0.0014 2.2370 1.364 0.5082 1.6560 0.2632 0.2685 0.3411 0.1432 0.94591995,00 0.0359 0.0005 2.4730 1.540 0.0427 3.1480 0.1544 0.1551 0.1021 0.0547 0.47972000,05 0.0345 0.0015 2.5550 2.094 0.5126 2.0820 0.1855 0.1898 ,0.0049 ,0.0802 0.97282005,10 0.0264 0.0016 1.1120 0.8607 0.7522 1.1410 0.2890 0.2927 0.2699 0.1800 0.9795

1935,2010 0.0360 0.0026 6.5970 4.941 2.7580 6.1130 0.0905 0.0962 0.1082 0.1361 0.9763

TABLE!4a:!Equal,Weighted!NYSE!Market!Portfolio!!!!!!!!!+!!!!!!!20!Single,Sort!Test!Portfolios!Built!Using!Equal,Weighted!SecuritiesTHE!BEHAVIOR!OF!THE!MARKET

Statistics

Statistics

Rm Rm � Rf¯�1

¯�0 RfRm�Rf

s(Rm)

¯�1

s(Rm)s(Rm) s(Rm � Rf )

s(�0) s(Rf ) t(Rm � Rf ) t( ¯�1) t( ¯�0) ⇢M (Rm) ⇢(Rm � Rf ) ⇢M (�1) ⇢M (�0) ⇢M (Rf )t(Rm)

20

! ! ! ! ! ! ! ! ! ! ! !! ! !

Period

1935,6/68 0.0109 0.0096 0.0044 0.0080 0.0013 0.2138 0.0986 0.0449 0.0450 ! !

1935,45 0.0115 0.0114 0.0077 0.0080 0.0001 0.1899 0.1282 0.0600 0.0600 ! !1946,55 0.0123 0.0114 0.0024 0.0091 0.0009 0.3078 0.0650 0.0370 0.0370 ! !1956,6/68 0.0092 0.0066 0.0032 0.0072 0.0026 0.1925 0.0930 0.0344 0.0345 ! !

1935,40 0.0092 0.0092 0.0039 0.0071 0.0001 0.1238 0.0534 0.0739 0.0739 ! !1941,45 0.0143 0.0141 0.0121 0.0090 0.0002 0.3709 0.3203 0.0379 0.0378 ! !1946,50 0.0082 0.0075 0.0048 0.0028 0.0007 0.1819 0.1167 0.0414 0.0413 ! !1951,55 0.0165 0.0152 0.0000 0.0155 0.0012 0.4794 ,0.0008 0.0318 0.0319 ! !1956,60 0.0085 0.0064 ,0.0024 0.0107 0.0021 0.1905 ,0.0708 0.0337 0.0339 ! !1961,6/68 0.0097 0.0068 0.0069 0.0048 0.0029 0.1928 0.1974 0.0350 0.0351 ! !

7/1968,2010 0.0088 0.0043 0.0019 0.0093 0.0045 0.0959 0.0419 0.0444 0.0444 ! !

1970,80 0.0078 0.0023 0.0030 0.0086 0.0055 0.0478 0.0615 0.0488 0.0490 ! !1980,90 0.0130 0.0060 ,0.0037 0.0172 0.0071 0.126 ,0.0779 0.0476 0.0480 ! !1990,00 0.0123 0.0082 0.0056 0.0056 0.0041 0.2167 0.1474 0.0379 0.0379 ! !2000,10 0.0034 0.0014 0.0019 0.0073 0.0021 0.0308 0.0426 0.0443 0.0444 ! !

1970,75 0.0034 ,0.0014 0.0001 0.0072 0.0048 ,0.0271 0.0019 0.0524 0.0528 ! !1975,80 0.0157 0.0097 0.0079 0.0124 0.0060 0.2122 0.1722 0.0457 0.0458 ! !1980,85 0.0147 0.0064 ,0.0041 0.0212 0.0083 0.149 ,0.0961 0.0430 0.0437 ! !1985,90 0.0132 0.0076 ,0.0038 0.0155 0.0056 0.150 ,0.0754 0.0505 0.0506 ! !1990,95 0.0106 0.0067 0.0072 0.0037 0.0040 0.1986 0.2136 0.0336 0.0336 ! !1995,00 0.0163 0.0120 0.0026 0.0106 0.0043 0.302 0.0662 0.0397 0.0397 ! !2000,05 0.0032 0.0010 0.0011 0.0103 0.0023 0.0254 0.0289 0.0384 0.0385 ! !2005,10 0.0041 0.0021 0.0028 0.0039 0.0019 0.0451 0.0585 0.0471 0.0471 ! !

1935,2010 0.0097 0.0066 0.0030 0.0087 0.0031 0.1482 0.0670 0.0446 0.0447 ! !

Period

1935,6/68 0.0489 0.0012 4.8620 4.276 1.8990 3.2830 ,0.0194 ,0.0164 0.0368 0.0000 0.9661

1935,45 0.0667 0.0002 2.2010 2.1750 1.5460 1.3680 ,0.0815 ,0.0814 ,0.0050 ,0.0769 0.63721946,55 0.0370 0.0004 3.6520 3.374 0.6658 2.6990 0.0116 0.0101 0.0621 ,0.0423 0.89231956,6/68 0.0380 0.0009 3.2860 2.351 0.9322 2.3130 0.1149 0.1207 0.0754 0.2354 0.8512

1935,40 0.0820 0.0002 1.0520 1.0440 0.5080 0.7304 ,0.1453 ,0.1445 ,0.0950 ,0.1019 0.43611941,45 0.0427 0.0001 2.9180 2.8770 2.0850 1.6310 0.1957 0.1941 0.1966 0.0333 0.72331946,50 0.0420 0.0003 1.5340 1.4120 0.8716 0.5075 0.0581 0.0551 0.0532 0.0578 0.91021951,55 0.0303 0.0004 4.0120 3.699 ,0.0056 3.9550 ,0.1387 ,0.1314 0.0579 ,0.2748 0.75561956,60 0.0268 0.0007 1.9610 1.467 ,0.5981 3.0950 0.1006 0.1152 0.0264 0.1372 0.65991961,6/68 0.0439 0.0008 2.6250 1.827 1.3720 1.0420 0.1061 0.1064 0.0761 0.2439 0.8900

7/1968,2010 0.0412 0.0025 4.4750 2.160 0.7919 5.0760 0.0676 0.0695 0.1453 0.1188 0.9605

1970,80 0.0509 0.0020 1.8350 0.547 0.5736 1.9410 0.0239 0.0253 0.1456 0.1092 0.89311980,90 0.0447 0.0023 3.1430 1.431 ,0.7567 4.4110 0.0647 0.0750 0.0989 0.0578 0.89031990,00 0.0366 0.0011 3.7280 2.488 1.2700 1.7470 ,0.0867 ,0.0849 0.1647 0.1145 0.90552000,10 0.0294 0.0016 0.8911 0.354 0.4685 2.8380 0.1825 0.1854 0.1688 0.0989 0.9778

1970,75 0.0569 0.0013 0.5462 ,0.228 0.0134 1.0800 0.0966 0.1058 0.1369 0.1635 0.82951975,80 0.0445 0.0023 2.9150 1.797 1.1510 2.3670 ,0.0320 ,0.0340 0.1481 ,0.0162 0.89641980,85 0.0448 0.0022 2.9040 1.240 ,0.6459 4.0050 0.0511 0.0778 0.0737 0.0419 0.83061985,90 0.0429 0.0010 2.2190 1.270 ,0.5810 3.0620 0.0862 0.0844 0.1160 0.0520 0.77271990,95 0.0357 0.0014 2.6910 1.684 1.2810 0.8816 ,0.1039 ,0.1042 0.1412 0.1149 0.94591995,00 0.0373 0.0005 3.4740 2.560 0.4309 2.4080 ,0.0801 ,0.0776 0.1804 0.1241 0.47972000,05 0.0270 0.0015 0.7153 0.215 0.2232 3.2440 0.0366 0.0436 0.0388 0.1650 0.97282005,10 0.0301 0.0016 0.7322 0.3824 0.4910 1.0940 0.2615 0.2618 0.2561 0.0340 0.9795

1935,2010 0.0447 0.0026 6.5800 4.458 1.7940 5.8790 0.0292 0.0346 0.1051 0.0559 0.9763

TABLE!4h:!Value,Weighted!NYSE!Market!Portfolio!!!!!!!!!+!!!!!!!5x5!Double,Sort!Test!Portfolios!Built!Using!Value,Weighted!SecuritiesTHE!BEHAVIOR!OF!THE!MARKET

Statistics

Statistics

Rm Rm � Rf¯�1

¯�0 RfRm�Rf

s(Rm)

¯�1



21

3.4 Variance decomposition

Following Fama-MacBeth (1973), I let φjt denote the estimation error such that φjt � γjt�γjt.Then, let spφjtq be the standard error of γjt in the cross-sectional regression at time t and

let s2pφjq denote the average of the s2pφjtq values for all t in the testing period. Lastly with

the sample variance of the monthly γjt estimates, s2pγjtq, I define s2pγjtq � s2pγjtq � s2pφjq

and F � s2pγjtq{s2pφjq (the F-statistics).

I will first describe the results in Table 5a. This is the base case with the 20 beta-sortedportfolios. As I include additional regressors in the model the F-statistics tend to decrease.This should be expected because as Fama-MacBeth (1973) explains the additional regressorsintroduce more colinearity and the error in the new regressors is likely correlated with theerror in the original regressors. Nonetheless, focusing on Panel D, the F-statistics tend tobe above the relevant critical values11 except for γ3. These results provide some reassurancethat the variation in γjt is not driven by error and likely correctly reflects variation in thetrue variable, γjt. The exception is for γ3, where the corresponding F-statistics tend to be

too low to reject the null hypothesis that s2pγ3tq � s2pφ3q. Nonetheless, I also find that theF-statistics are larger for the 7/1968-2010 testing period than for the 1935-6/1968 testingperiod.

In Table 5e, I use the value-weighted NYSE porfolio returns as a proxy for the marketportfolio returns, the 5 � 5 dual-sorted test portfolios, and regressors constructed usingequal-weighted averages of the underlying security estimates. Focusing again on Panel D, Ifind that the F-statistics are much greater. In particular, for the 1935-2010 testing period,

s2pγ0tq{s2pφ0q � 2.87, s2pγ1tq{s2pφ1q � 2.56, s2pγ2tq{s2pφ2q � 1.97. These results providesome evidence that estimates γ0, γ1 and γ2 are likely accurate (and more so than in Ta-

ble 5a). However, notice that s2pγ3tq{s2pφ3q � 4.18 , 4.44, and 4.36 for the 1935-6/1968,7/1968-2010, and 1935-2010 testing periods (respectively). Thus with the 5 � 5 dual-sorttest portfolios I find that Epγ3tq is more accurately estimated than the other coefficients andit is also more accurately estimated compared to when I use the 20 beta-sorted test porfoliosof Fama-MacBeth (1973). Given the results in Table 3e which show that ¯γ3 is significantlydifferent from zero the results on Table 5e cast additional doubt on the validity of the assetpricing model. Lastly, on Table 5e we can also see that the F-statistics are greater for the7/1968-2010 testing period than for the 1935-6/1968 testing period. This is perhaps hintingthat the coefficients in the cross-sectional regressions tend to be better estimated in latertime periods.

11The F-stat has degrees of freedom tn � 1, npP �Kqu where n is the number of months in the testingperiod, P is the number of test-portfolios, and K is the number of coefficients γj in the regression. Therelevant critical value for a test at a 5% level is between 1.25 and 1.35.

22

!!

!!

!!

!

Period

Period

!!

!!

!!

!!

!Pane

l!A!

!!

!!

!!

!Pane

l!C!

!!

!!

!!

!193516/68

0.0010

0.0003

0.0013

4.1530

0.0040

0.0003

0.0043

14.3600

193516/68

0.0011

0.0007

0.0019

2.5860

0.0039

0.0015

0.0055

3.5910

1935145

0.0016

0.0008

0.0023

3.1240

0.0088

0.0007

0.0095

12.9700

1935145

0.0019

0.0013

0.0032

2.4850

0.0085

0.0029

0.0114

3.9470

1946155

0.0006

0.0001

0.0007

8.4480

0.0017

0.0001

0.0017

24.2400

1946155

0.0009

0.0002

0.0012

4.9260

0.0022

0.0007

0.0029

4.3780

195616/68

0.0008

0.0001

0.0009

7.7540

0.0018

0.0001

0.0019

16.9500

195616/68

0.0006

0.0006

0.0012

2.0570

0.0013

0.0010

0.0023

2.3040

1935140

0.0024

0.0012

0.0035

3.0160

0.0128

0.0012

0.0140

12.0400

1935140

0.0030

0.0017

0.0047

2.7630

0.0147

0.0038

0.0185

4.8720

1941145

0.0007

0.0003

0.0010

3.7860

0.0041

0.0002

0.0043

19.0500

1941145

0.0006

0.0008

0.0014

1.8250

0.0014

0.0018

0.0032

1.7460

1946150

0.0009

0.0001

0.0010

11.8200

0.0023

0.0001

0.0023

31.4600

1946150

0.0014

0.0003

0.0017

5.8420

0.0029

0.0009

0.0038

4.3450

1951155

0.0003

0.0001

0.0004

4.6550

0.0011

0.0001

0.0012

17.0400

1951155

0.0005

0.0002

0.0007

3.6190

0.0015

0.0004

0.0019

4.5540

1956160

0.0003

0.0001

0.0004

4.3960

0.0010

0.0001

0.0011

13.5600

1956160

0.0004

0.0005

0.0010

1.8150

0.0003

0.0010

0.0013

1.2550

196116/68

0.0010

0.0001

0.0012

8.7520

0.0021

0.0001

0.0023

17.3200

196116/68

0.0008

0.0006

0.0014

2.1770

0.0019

0.0010

0.0029

2.8950

7/196812010

0.0011

0.0002

0.0013

7.5540

0.0034

0.0002

0.0035

19.6600

7/196812010

0.0012

0.0007

0.0019

2.7380

0.0041

0.0025

0.0065

2.6340

1970180

0.0012

0.0002

0.0014

7.1430

0.0042

0.0002

0.0044

20.4300

1970180

0.0014

0.0009

0.0022

2.5770

0.0026

0.0032

0.0058

1.8150

1980190

0.0013

0.0002

0.0015

7.8760

0.0032

0.0002

0.0034

16.7000

1980190

0.0012

0.0007

0.0019

2.7370

0.0072

0.0031

0.0103

3.3380

1990100

0.0013

0.0002

0.0015

7.1170

0.0030

0.0002

0.0032

14.9200

1990100

0.0011

0.0004

0.0016

3.5120

0.0030

0.0016

0.0046

2.9120

2000110

0.0009

0.0001

0.0010

7.5570

0.0035

0.0001

0.0037

27.6800

2000110

0.0014

0.0009

0.0023

2.6580

0.0041

0.0027

0.0068

2.4960

1970175

0.0015

0.0002

0.0017

7.4680

0.0041

0.0002

0.0044

17.8500

1970175

0.0019

0.0009

0.0027

3.1290

0.0035

0.0025

0.0060

2.3780

1975180

0.0011

0.0002

0.0013

6.6240

0.0044

0.0002

0.0046

21.5700

1975180

0.0010

0.0010

0.0020

2.0070

0.0012

0.0043

0.0055

1.2860

1980185

0.0012

0.0002

0.0013

8.8620

0.0029

0.0002

0.0030

18.9200

1980185

0.0011

0.0009

0.0020

2.2390

0.0033

0.0035

0.0069

1.9530

1985190

0.0014

0.0002

0.0016

7.2270

0.0032

0.0002

0.0035

15.0700

1985190

0.0012

0.0005

0.0017

3.4710

0.0109

0.0025

0.0134

5.2820

1990195

0.0013

0.0003

0.0016

6.0130

0.0031

0.0003

0.0034

12.8800

1990195

0.0009

0.0004

0.0012

3.4470

0.0033

0.0015

0.0048

3.1280

1995100

0.0012

0.0001

0.0013

9.5910

0.0025

0.0001

0.0027

19.2300

1995100

0.0012

0.0005

0.0017

3.3990

0.0025

0.0015

0.0040

2.7150

2000105

0.0011

0.0001

0.0012

8.7580

0.0028

0.0001

0.0030

21.5300

2000105

0.0015

0.0007

0.0023

3.0420

0.0020

0.0020

0.0040

1.9770

2005110

0.0006

0.0001

0.0007

5.9350

0.0038

0.0001

0.0039

34.4700

2005110

0.0012

0.0009

0.0021

2.2690

0.0056

0.0034

0.0089

2.6650

193512010

0.0011

0.0002

0.0013

5.5530

0.0037

0.0002

0.0039

16.6500

193512010

0.0012

0.0007

0.0019

2.6670

0.0040

0.0021

0.0061

2.9440

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!B!

!!

!!

!!

!Pane

l!D!

!!

!!

!!

!193516/68

0.0014

0.0013

0.0027

2.0370

0.0080

0.0066

0.0146

2.2190

193516/68

0.0009

0.0035

0.0044

1.2730

0.0072

0.0071

0.0144

2.0150

1935145

0.0019

0.0020

0.0039

1.9780

0.0117

0.0107

0.0223

2.0950

1935145

0.0008

0.0064

0.0072

1.1200

0.0093

0.0119

0.0211

1.7810

1946155

0.0004

0.0006

0.0010

1.6710

0.0050

0.0026

0.0076

2.9710

1946155

0.0002

0.0015

0.0017

1.1320

0.0049

0.0026

0.0075

2.8940

195616/68

0.0017

0.0013

0.0030

2.2420

0.0073

0.0062

0.0136

2.1790

195616/68

0.0016

0.0024

0.0041

1.6660

0.0074

0.0066

0.0140

2.1260

1935140

0.0022

0.0028

0.0051

1.7810

0.0200

0.0153

0.0353

2.3090

1935140

0.0003

0.0079

0.0082

1.0330

0.0159

0.0170

0.0330

1.9360

1941145

0.0016

0.0009

0.0025

2.7560

0.0021

0.0052

0.0073

1.4080

1941145

0.0015

0.0046

0.0061

1.3190

0.0017

0.0058

0.0075

1.2920

1946150

0.0007

0.0006

0.0013

2.1150

0.0066

0.0025

0.0091

3.5890

1946150

0.0006

0.0017

0.0024

1.3630

0.0066

0.0026

0.0092

3.4950

1951155

0.0002

0.0006

0.0008

1.2560

0.0036

0.0026

0.0062

2.3880

1951155

10.000

20.0012

0.0010

0.8148

0.0033

0.0026

0.0059

2.3010

1956160

0.0002

0.0005

0.0007

1.5000

0.0021

0.0023

0.0044

1.9300

1956160

0.0007

0.0016

0.0023

1.4450

0.0017

0.0026

0.0043

1.6680

196116/68

0.0025

0.0019

0.0044

2.3230

0.0106

0.0089

0.0194

2.1930

196116/68

0.0022

0.0030

0.0052

1.7350

0.0109

0.0093

0.0201

2.1750

7/196812010

0.0030

0.0011

0.0041

3.6050

0.0161

0.0063

0.0224

3.5560

7/196812010

0.0025

0.0028

0.0054

1.8960

0.0150

0.0085

0.0235

2.7670

1970180

0.0059

0.0023

0.0081

3.5990

0.0297

0.0116

0.0413

3.5480

1970180

0.0056

0.0048

0.0104

2.1830

0.0235

0.0150

0.0384

2.5690

1980190

0.0043

0.0013

0.0056

4.3010

0.0241

0.0067

0.0308

4.5900

1980190

0.0030

0.0029

0.0059

2.0240

0.0224

0.0101

0.0325

3.2090

1990100

0.0013

0.0008

0.0021

2.6320

0.0080

0.0056

0.0136

2.4150

1990100

0.0004

0.0026

0.0031

1.1630

0.0068

0.0077

0.0145

1.8930

2000110

0.0008

0.0004

0.0012

3.2420

0.0068

0.0026

0.0094

3.6610

2000110

0.0008

0.0015

0.0023

1.5360

0.0081

0.0038

0.0120

3.1060

1970175

0.0057

0.0023

0.0080

3.4220

0.0243

0.0126

0.0369

2.9190

1970175

0.0045

0.0066

0.0111

1.6910

0.0223

0.0140

0.0362

2.5940

1975180

0.0075

0.0022

0.0097

4.3560

0.0386

0.0111

0.0497

4.4970

1975180

0.0077

0.0033

0.0109

3.3580

0.0293

0.0161

0.0453

2.8230

1980185

0.0045

0.0012

0.0057

4.5910

0.0220

0.0055

0.0275

4.9910

1980185

0.0038

0.0019

0.0057

3.0400

0.0225

0.0101

0.0326

3.2380

1985190

0.0039

0.0012

0.0052

4.1590

0.0248

0.0073

0.0321

4.3900

1985190

0.0020

0.0037

0.0057

1.5380

0.0220

0.0092

0.0312

3.3850

1990195

0.0015

0.0011

0.0026

2.3740

0.0073

0.0074

0.0147

1.9930

1990195

10.000

20.0038

0.0037

0.9554

0.0049

0.0108

0.0156

1.4530

1995100

0.0012

0.0004

0.0016

3.6550

0.0085

0.0031

0.0117

3.7220

1995100

0.0010

0.0011

0.0021

1.9050

0.0090

0.0036

0.0126

3.5080

2000105

0.0007

0.0004

0.0011

2.5060

0.0046

0.0032

0.0078

2.4200

2000105

0.0011

0.0014

0.0025

1.7970

0.0049

0.0038

0.0088

2.2940

2005110

0.0010

0.0003

0.0013

4.5310

0.0083

0.0017

0.0100

5.8940

2005110

0.0006

0.0015

0.0020

1.3910

0.0102

0.0037

0.0138

3.7690

193512010

0.0023

0.0012

0.0035

2.8560

0.0125

0.0064

0.0190

2.9510

193512010

0.0018

0.0031

0.0049

1.5890

0.0116

0.0079

0.0195

2.4660

TABLE!5a:!Equ

al1W



ortfolios!Bu

ilt!Using!Equ

al1W

eighted!Securitie

sCO

MPO

NEN

TS!OF!TH

E!VARIANCE

S!OF!TH

E

FF

FF

s2(�

0)

s2(�

0)

s2(�

0)

s2(�

1)

s2(�

1)

s2(�

1)

s2(�

0)

s2(�

0)

s2(�

0)

s2(�

1)

s2(�

1)

s2(�

1)

�j,

t

23

Period

! Pane

l!A!

!!

!!

!!

!Pane

l!C!

!!

!!

!!

!193516/68

11

11

11

11

193516/68

11

11

0.1079

0.4617

0.5696

1.2340

1935145

11

11

11

11

1935145

11

11

0.0324

0.3475

0.3799

1.0930

1946155

11

11

11

11

1946155

11

11

0.2059

0.2838

0.4896

1.7260

195616/68

11

11

11

11

195616/68

11

11

0.0954

0.7037

0.7991

1.1360

1935140

11

11

11

11

1935140

11

11

10.070

40.3324

0.2620

0.7882

1941145

11

11

11

11

1941145

11

11

0.1590

0.3654

0.5244

1.4350

1946150

11

11

11

11

1946150

11

11

0.2352

0.3205

0.5557

1.7340

1951155

11

11

11

11

1951155

11

11

0.1845

0.2470

0.4315

1.7470

1956160

11

11

11

11

1956160

11

11

0.2057

0.7499

0.9556

1.2740

196116/68

11

11

11

11

196116/68

11

11

0.0284

0.6729

0.7012

1.0420

7/196812010

11

11

11

11

7/196812010

11

11

0.4087

0.7498

1.1580

1.5450

1970180

11

11

11

11

1970180

11

11

0.4060

0.9703

1.3760

1.4180

1980190

11

11

11

11

1980190

11

11

0.4909

0.8171

1.3080

1.6010

1990100

11

11

11

11

1990100

11

11

0.2101

0.3949

0.6050

1.5320

2000110

11

11

11

11

2000110

11

11

0.6719

0.9154

1.5870

1.7340

1970175

11

11

11

11

1970175

11

11

0.7125

0.9025

1.6150

1.7890

1975180

11

11

11

11

1975180

11

11

0.2310

1.1590

1.3900

1.1990

1980185

11

11

11

11

1980185

11

11

0.3482

1.0210

1.3690

1.3410

1985190

11

11

11

11

1985190

11

11

0.6158

0.5996

1.2150

2.0270

1990195

11

11

11

11

1990195

11

11

0.0929

0.3083

0.4011

1.3010

1995100

11

11

11

11

1995100

11

11

0.2751

0.4581

0.7332

1.6000

2000105

11

11

11

11

2000105

11

11

0.5578

0.6815

1.2390

1.8190

2005110

11

11

11

11

2005110

11

11

0.7250

1.1160

1.8410

1.6500

193512010

11

11

11

11

193512010

11

11

0.2754

0.6230

0.8984

1.4420

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!B!

!!

!!

!!

!Pane

l!D!

!!

!!

!!

!193516/68

0.0010

0.0016

0.0026

1.6010

11

11

193516/68

0.0008

0.0027

0.0034

1.2930

0.0229

0.6701

0.6930

1.0340

1935145

0.0015

0.0029

0.0044

1.5050

11

11

1935145

0.0010

0.0056

0.0066

1.1780

10.104

80.7357

0.6309

0.8576

1946155

0.0005

0.0005

0.0010

1.9410

11

11

1946155

0.0003

0.0007

0.0010

1.3710

0.0489

0.3996

0.4485

1.1220

195616/68

0.0009

0.0014

0.0024

1.6670

11

11

195616/68

0.0010

0.0016

0.0026

1.5950

0.1089

0.8292

0.9381

1.1310

1935140

0.0007

0.0043

0.0050

1.1710

11

11

1935140

10.000

50.0079

0.0075

0.9405

10.075

30.7200

0.6447

0.8954

1941145

0.0024

0.0013

0.0037

2.8590

11

11

1941145

0.0029

0.0029

0.0057

1.9910

10.129

10.7544

0.6253

0.8289

1946150

0.0005

0.0005

0.0010

2.0980

11

11

1946150

0.0003

0.0007

0.0011

1.4330

0.0376

0.4629

0.5005

1.0810

1951155

0.0005

0.0006

0.0010

1.8120

11

11

1951155

0.0002

0.0007

0.0009

1.2840

0.0619

0.3364

0.3982

1.1840

1956160

0.0002

0.0005

0.0007

1.4770

11

11

1956160

0.0004

0.0007

0.0011

1.5230

0.2822

0.9704

1.2530

1.2910

196116/68

0.0014

0.0020

0.0034

1.6980

11

11

196116/68

0.0014

0.0022

0.0036

1.6120

10.002

40.7350

0.7326

0.9967

7/196812010

0.0029

0.0017

0.0045

2.7340

11

11

7/196812010

0.0022

0.0027

0.0049

1.8020

0.0712

0.9100

0.9812

1.0780

1970180

0.0061

0.0029

0.0090

3.1120

11

11

1970180

0.0052

0.0040

0.0091

2.3050

10.080

51.1460

1.0650

0.9297

1980190

0.0029

0.0017

0.0046

2.6490

11

11

1980190

0.0011

0.0032

0.0044

1.3460

10.049

41.0310

0.9816

0.9520

1990100

0.0015

0.0018

0.0032

1.8550

11

11

1990100

0.0002

0.0041

0.0043

1.0550

10.004

40.6669

0.6625

0.9934

2000110

0.0012

0.0007

0.0019

2.7100

11

11

2000110

0.0009

0.0008

0.0017

2.1780

0.2870

0.9845

1.2720

1.2920

1970175

0.0064

0.0032

0.0097

2.9830

11

11

1970175

0.0049

0.0051

0.0099

1.9650

0.0130

1.2730

1.2860

1.0100

1975180

0.0077

0.0027

0.0104

3.8230

11

11

1975180

0.0070

0.0030

0.0101

3.3330

10.234

01.1260

0.8919

0.7922

1980185

0.0027

0.0012

0.0039

3.2270

11

11

1980185

0.0024

0.0013

0.0037

2.8440

0.1015

1.0090

1.1110

1.1010

1985190

0.0029

0.0021

0.0050

2.3930

11

11

1985190

10.000

10.0048

0.0047

0.9796

10.170

80.9975

0.8268

0.8288

1990195

0.0016

0.0024

0.0040

1.6720

11

11

1990195

10.000

40.0066

0.0062

0.9398

10.180

70.7735

0.5928

0.7664

1995100

0.0013

0.0009

0.0022

2.4610

11

11

1995100

0.0008

0.0010

0.0019

1.8210

0.1164

0.4894

0.6058

1.2380

2000105

0.0015

0.0009

0.0025

2.6370

11

11

2000105

0.0011

0.0010

0.0021

2.0880

0.3758

0.7527

1.1280

1.4990

2005110

0.0007

0.0004

0.0011

2.7910

11

11

2005110

0.0006

0.0004

0.0010

2.3420

0.2167

1.1760

1.3920

1.1840

193512010

0.0020

0.0017

0.0037

2.2380

11

11

193512010

0.0016

0.0027

0.0043

1.5790

0.0494

0.8044

0.8538

1.0610

FF

FF

TABLE!5a:!Equ

al1W



ortfolios!Bu

ilt!Using!Equ

al1W

eighted!Securitie

sCO

MPO

NEN

TS!OF!TH

E!VARIANCE

S!OF!TH

E!!!!!!!!!!!!!(con

t.)

s2(�

2)

s2(�

2)

s2(�

2)

s2(�

3)

s2(�

3)

s2(�

3)

s2(�

2)

s2(�

2)

s2(�

2)

s2(�

3)

s2(�

3)

s2(�

3)

�j,

t

24

!!

!!

!!

!

Period

Period

!!

!!

!!

!!

!Pane

l!A!

!!

!!

!!

!Pane

l!C!

!!

!!

!!

!193516/68

0.0010

0.0003

0.0013

4.1890

0.0041

0.0003

0.0044

15.1500

193516/68

0.0012

0.0003

0.0015

4.6120

0.0030

0.0007

0.0037

5.2790

1935145

0.0015

0.0007

0.0022

3.1310

0.0089

0.0007

0.0096

14.4200

1935145

0.0017

0.0007

0.0024

3.4130

0.0056

0.0015

0.0071

4.7480

1946155

0.0006

0.0001

0.0007

7.4270

0.0015

0.0001

0.0015

18.7800

1946155

0.0007

0.0001

0.0008

8.7940

0.0022

0.0002

0.0024

11.1300

195616/68

0.0008

0.0001

0.0010

7.3540

0.0019

0.0001

0.0020

16.4000

195616/68

0.0010

0.0002

0.0011

7.1520

0.0013

0.0004

0.0017

4.4920

1935140

0.0021

0.0011

0.0032

3.0260

0.0131

0.0010

0.0141

13.6800

1935140

0.0024

0.0010

0.0034

3.3470

0.0091

0.0020

0.0111

5.5100

1941145

0.0007

0.0003

0.0010

3.7330

0.0041

0.0002

0.0043

18.8400

1941145

0.0009

0.0003

0.0013

3.7590

0.0015

0.0009

0.0024

2.7500

1946150

0.0008

0.0001

0.0009

11.4800

0.0019

0.0001

0.0019

26.8800

1946150

0.0009

0.0001

0.0010

12.7000

0.0030

0.0003

0.0033

12.9800

1951155

0.0003

0.0001

0.0004

4.0590

0.0011

0.0001

0.0012

12.6200

1951155

0.0005

0.0001

0.0006

5.7810

0.0014

0.0002

0.0016

8.7310

1956160

0.0004

0.0001

0.0005

4.2280

0.0011

0.0001

0.0012

11.7400

1956160

0.0005

0.0001

0.0006

4.3340

0.0011

0.0002

0.0014

5.9130

196116/68

0.0011

0.0001

0.0012

8.5090

0.0024

0.0001

0.0025

17.7000

196116/68

0.0012

0.0002

0.0014

8.1580

0.0015

0.0005

0.0019

4.0130

7/196812010

0.0011

0.0002

0.0013

6.9250

0.0032

0.0002

0.0034

17.9100

7/196812010

0.0015

0.0003

0.0017

6.9520

0.0027

0.0009

0.0036

4.0200

1970180

0.0014

0.0002

0.0016

8.2040

0.0042

0.0002

0.0044

21.3800

1970180

0.0021

0.0003

0.0024

7.5400

0.0023

0.0014

0.0037

2.6090

1980190

0.0013

0.0002

0.0015

7.1690

0.0032

0.0002

0.0034

16.1600

1980190

0.0016

0.0003

0.0019

6.9040

0.0036

0.0011

0.0047

4.3360

1990100

0.0011

0.0002

0.0014

5.8720

0.0026

0.0002

0.0029

12.0800

1990100

0.0015

0.0002

0.0018

7.8050

0.0030

0.0005

0.0035

6.8310

2000110

0.0008

0.0002

0.0009

5.3400

0.0032

0.0002

0.0033

19.1200

2000110

0.0011

0.0002

0.0014

5.7150

0.0028

0.0006

0.0034

5.4020

1970175

0.0018

0.0002

0.0020

10.0800

0.0041

0.0002

0.0043

20.9000

1970175

0.0027

0.0004

0.0031

8.1390

0.0025

0.0017

0.0042

2.4520

1975180

0.0011

0.0002

0.0013

6.4470

0.0042

0.0002

0.0044

19.3400

1975180

0.0015

0.0003

0.0018

6.2690

0.0022

0.0012

0.0034

2.7690

1980185

0.0011

0.0002

0.0012

7.3500

0.0029

0.0002

0.0030

17.2500

1980185

0.0014

0.0002

0.0016

6.8360

0.0027

0.0011

0.0038

3.3990

1985190

0.0014

0.0002

0.0017

7.3380

0.0033

0.0002

0.0036

15.5600

1985190

0.0017

0.0003

0.0020

6.8350

0.0042

0.0011

0.0053

4.8040

1990195

0.0011

0.0003

0.0014

5.1970

0.0027

0.0003

0.0030

10.8500

1990195

0.0014

0.0003

0.0017

6.1710

0.0019

0.0006

0.0025

4.3950

1995100

0.0011

0.0002

0.0013

7.3430

0.0024

0.0002

0.0026

14.6600

1995100

0.0015

0.0002

0.0017

10.6100

0.0038

0.0004

0.0042

10.2600

2000105

0.0009

0.0002

0.0010

5.6120

0.0024

0.0002

0.0026

14.1700

2000105

0.0013

0.0002

0.0015

7.1430

0.0025

0.0005

0.0030

5.8600

2005110

0.0006

0.0002

0.0007

4.7680

0.0035

0.0001

0.0037

24.8800

2005110

0.0008

0.0002

0.0010

4.2790

0.0028

0.0007

0.0035

5.0710

193512010

0.0010

0.0002

0.0013

5.3860

0.0036

0.0002

0.0038

16.4200

193512010

0.0013

0.0003

0.0016

5.7820

0.0028

0.0008

0.0036

4.4950

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!B!

!!

!!

!!

!Pane

l!D!

!!

!!

!!

!193516/68

0.0009

0.0016

0.0025

1.5600

0.0036

0.0078

0.0114

1.4610

193516/68

0.0013

0.0019

0.0032

1.6900

0.0042

0.0071

0.0114

1.5940

1935145

0.0009

0.0026

0.0036

1.3510

0.0003

0.0138

0.0141

1.0190

1935145

0.0008

0.0031

0.0039

1.2530

0.0018

0.0128

0.0146

1.1380

1946155

0.0005

0.0006

0.0011

1.8260

0.0066

0.0025

0.0091

3.6020

1946155

0.0003

0.0008

0.0011

1.3530

0.0056

0.0024

0.0080

3.3140

195616/68

0.0012

0.0015

0.0027

1.7930

0.0041

0.0068

0.0109

1.6050

195616/68

0.0025

0.0017

0.0042

2.5020

0.0054

0.0060

0.0113

1.8970

1935140

0.0010

0.0039

0.0049

1.2540

0.0008

0.0206

0.0213

1.0370

1935140

0.0010

0.0043

0.0053

1.2220

0.0029

0.0189

0.0218

1.1550

1941145

0.0009

0.0011

0.0020

1.7870

10.000

10.0058

0.0057

0.9761

1941145

0.0006

0.0016

0.0023

1.3870

0.0006

0.0056

0.0062

1.1100

1946150

0.0007

0.0004

0.0011

2.7790

0.0071

0.0015

0.0086

5.6640

1946150

0.0005

0.0007

0.0012

1.7660

0.0062

0.0015

0.0077

5.0630

1951155

0.0003

0.0008

0.0011

1.3840

0.0061

0.0035

0.0096

2.7170

1951155

0.0001

0.0009

0.0010

1.0610

0.0050

0.0033

0.0082

2.5170

1956160

0.0005

0.0007

0.0011

1.7170

0.0039

0.0030

0.0069

2.2970

1956160

0.0004

0.0008

0.0012

1.5140

0.0041

0.0027

0.0068

2.4970

196116/68

0.0017

0.0020

0.0037

1.8160

0.0043

0.0093

0.0136

1.4660

196116/68

0.0039

0.0023

0.0062

2.6930

0.0063

0.0081

0.0144

1.7730

7/196812010

0.0024

0.0012

0.0035

3.0350

0.0131

0.0062

0.0194

3.1040

7/196812010

0.0044

0.0014

0.0058

4.0740

0.0142

0.0056

0.0198

3.5380

1970180

0.0049

0.0022

0.0071

3.1830

0.0225

0.0108

0.0333

3.0940

1970180

0.0087

0.0026

0.0112

4.3820

0.0232

0.0093

0.0325

3.5000

1980190

0.0038

0.0014

0.0052

3.7920

0.0192

0.0070

0.0262

3.7650

1980190

0.0075

0.0016

0.0092

5.6610

0.0220

0.0063

0.0283

4.4820

1990100

0.0012

0.0008

0.0020

2.3820

0.0084

0.0059

0.0143

2.4360

1990100

0.0033

0.0011

0.0044

4.1060

0.0096

0.0051

0.0147

2.8720

2000110

0.0008

0.0005

0.0013

2.7170

0.0102

0.0030

0.0132

4.3900

2000110

0.0009

0.0006

0.0015

2.5480

0.0096

0.0027

0.0123

4.6050

1970175

0.0047

0.0022

0.0069

3.1850

0.0183

0.0109

0.0292

2.6790

1970175

0.0084

0.0031

0.0115

3.7280

0.0199

0.0097

0.0296

3.0500

1975180

0.0062

0.0023

0.0086

3.6670

0.0291

0.0110

0.0401

3.6370

1975180

0.0097

0.0022

0.0118

5.4270

0.0296

0.0094

0.0390

4.1520

1980185

0.0049

0.0016

0.0065

4.0380

0.0225

0.0072

0.0297

4.1190

1980185

0.0076

0.0016

0.0091

5.8510

0.0225

0.0061

0.0287

4.6850

1985190

0.0026

0.0010

0.0035

3.6040

0.0146

0.0059

0.0206

3.4690

1985190

0.0069

0.0015

0.0085

5.4760

0.0194

0.0059

0.0253

4.2850

1990195

0.0010

0.0012

0.0021

1.8280

0.0065

0.0083

0.0148

1.7780

1990195

0.0042

0.0014

0.0057

3.9890

0.0093

0.0074

0.0167

2.2430

1995100

0.0014

0.0004

0.0018

4.3300

0.0099

0.0026

0.0125

4.7740

1995100

0.0021

0.0006

0.0027

4.5600

0.0095

0.0021

0.0116

5.4140

2000105

0.0008

0.0005

0.0012

2.7170

0.0072

0.0031

0.0104

3.2950

2000105

0.0008

0.0006

0.0014

2.3820

0.0064

0.0027

0.0091

3.3960

2005110

0.0008

0.0005

0.0013

2.7960

0.0120

0.0026

0.0146

5.5590

2005110

0.0011

0.0005

0.0016

3.0360

0.0118

0.0024

0.0142

5.8660

193512010

0.0017

0.0014

0.0031

2.2670

0.0089

0.0069

0.0159

2.2880

193512010

0.0030

0.0016

0.0047

2.8650

0.0098

0.0063

0.0161

2.5620

TABLE!5e:!Equ

al1W


ortfolio!!!!!!!!!+!!!!!!!5x5!Dou

ble1Sort!Test!P

ortfolios!Bu

ilt!Using!Equ

al1W

eighted!Securitie

sCO

MPO

NEN

TS!OF!TH

E!VARIANCE

S!OF!TH

E

FF

FF

s2(�

0)

s2(�

0)

s2(�

0)

s2(�

1)

s2(�

1)

s2(�

1)

s2(�

0)

s2(�

0)

s2(�

0)

s2(�

1)

s2(�

1)

s2(�

1)

�j,

t

25

Period

! Pane

l!A!

!!

!!

!!

!Pane

l!C!

!!

!!

!!

!193516/68

11

11

11

11

193516/68

11

11

0.3271

0.0930

0.4201

4.5160

1935145

11

11

11

11

1935145

11

11

0.1770

0.0943

0.2713

2.8770

1946155

11

11

11

11

1946155

11

11

0.1846

0.0517

0.2363

4.5710

195616/68

11

11

11

11

195616/68

11

11

0.5450

0.1250

0.6700

5.3600

1935140

11

11

11

11

1935140

11

11

0.2016

0.0780

0.2795

3.5850

1941145

11

11

11

11

1941145

11

11

0.1398

0.1136

0.2534

2.2310

1946150

11

11

11

11

1946150

11

11

0.1817

0.0466

0.2283

4.8960

1951155

11

11

11

11

1951155

11

11

0.1868

0.0568

0.2436

4.2900

1956160

11

11

11

11

1956160

11

11

0.2496

0.0893

0.3388

3.7950

196116/68

11

11

11

11

196116/68

11

11

0.7318

0.1488

0.8806

5.9180

7/196812010

11

11

11

11

7/196812010

11

11

0.6471

0.1961

0.8432

4.3000

1970180

11

11

11

11

1970180

11

11

1.1600

0.3399

1.5000

4.4140

1980190

11

11

11

11

1980190

11

11

0.4805

0.2146

0.6951

3.2390

1990100

11

11

11

11

1990100

11

11

0.5193

0.0770

0.5963

7.7440

2000110

11

11

11

11

2000110

11

11

0.5151

0.1371

0.6521

4.7580

1970175

11

11

11

11

1970175

11

11

1.5310

0.4620

1.9920

4.3130

1975180

11

11

11

11

1975180

11

11

0.7214

0.2485

0.9700

3.9030

1980185

11

11

11

11

1980185

11

11

0.5700

0.2312

0.8011

3.4650

1985190

11

11

11

11

1985190

11

11

0.3111

0.2147

0.5258

2.4490

1990195

11

11

11

11

1990195

11

11

0.3553

0.0764

0.4316

5.6520

1995100

11

11

11

11

1995100

11

11

0.6097

0.0703

0.6800

9.6720

2000105

11

11

11

11

2000105

11

11

0.6063

0.1036

0.7098

6.8540

2005110

11

11

11

11

2005110

11

11

0.4238

0.1575

0.5813

3.6910

193512010

11

11

11

11

193512010

11

11

0.5063

0.1507

0.6571

4.3590

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!B!

!!

!!

!!

!Pane

l!D!

!!

!!

!!

!193516/68

0.0008

0.0019

0.0027

1.4250

11

11

193516/68

0.0006

0.0021

0.0027

1.3160

0.3581

0.1124

0.4704

4.1860

1935145

0.0008

0.0035

0.0043

1.2150

11

11

1935145

0.0007

0.0040

0.0047

1.1710

0.1972

0.1161

0.3134

2.6990

1946155

0.0007

0.0005

0.0012

2.3700

11

11

1946155

0.0003

0.0006

0.0009

1.5170

0.1498

0.0677

0.2175

3.2130

195616/68

0.0008

0.0015

0.0024

1.5600

11

11

195616/68

0.0009

0.0015

0.0024

1.5850

0.6392

0.1449

0.7841

5.4120

1935140

0.0005

0.0053

0.0058

1.0930

11

11

1935140

0.0009

0.0060

0.0069

1.1450

0.2627

0.0980

0.3607

3.6800

1941145

0.0011

0.0014

0.0025

1.8250

11

11

1941145

0.0005

0.0016

0.0021

1.3290

0.1101

0.1376

0.2476

1.8000

1946150

0.0006

0.0003

0.0008

3.1290

11

11

1946150

0.0003

0.0004

0.0007

1.7340

0.1623

0.0742

0.2365

3.1880

1951155

0.0009

0.0008

0.0016

2.0990

11

11

1951155

0.0003

0.0008

0.0011

1.4190

0.1364

0.0612

0.1977

3.2280

1956160

0.0005

0.0006

0.0011

1.7650

11

11

1956160

0.0002

0.0006

0.0009

1.3810

0.2045

0.0953

0.2999

3.1460

196116/68

0.0011

0.0021

0.0032

1.5160

11

11

196116/68

0.0014

0.0021

0.0035

1.6360

0.9185

0.1779

1.0960

6.1620

7/196812010

0.0022

0.0016

0.0039

2.3790

11

11

7/196812010

0.0027

0.0017

0.0044

2.5860

0.7621

0.2217

0.9838

4.4370

1970180

0.0039

0.0025

0.0064

2.5280

11

11

1970180

0.0049

0.0025

0.0074

3.0070

1.3350

0.3769

1.7120

4.5430

1980190

0.0025

0.0018

0.0043

2.3880

11

11

1980190

0.0047

0.0020

0.0067

3.4000

0.6821

0.2420

0.9241

3.8190

1990100

0.0020

0.0019

0.0039

2.0790

11

11

1990100

0.0019

0.0021

0.0039

1.8990

0.6143

0.1061

0.7204

6.7900

2000110

0.0019

0.0008

0.0027

3.4340

11

11

2000110

0.0012

0.0008

0.0020

2.6120

0.4606

0.1347

0.5953

4.4200

1970175

0.0042

0.0027

0.0069

2.5800

11

11

1970175

0.0045

0.0029

0.0074

2.5350

1.7440

0.5428

2.2870

4.2140

1975180

0.0048

0.0026

0.0074

2.8710

11

11

1975180

0.0064

0.0022

0.0086

3.9000

0.7769

0.2393

1.0160

4.2470

1980185

0.0031

0.0016

0.0047

2.9280

11

11

1980185

0.0042

0.0014

0.0056

4.0340

0.6642

0.2335

0.8977

3.8440

1985190

0.0017

0.0018

0.0034

1.9320

11

11

1985190

0.0047

0.0023

0.0071

3.0300

0.6026

0.2676

0.8702

3.2520

1990195

0.0017

0.0028

0.0045

1.6110

11

11

1990195

0.0026

0.0030

0.0056

1.8490

0.5300

0.1048

0.6349

6.0560

1995100

0.0021

0.0007

0.0029

3.9520

11

11

1995100

0.0009

0.0008

0.0017

2.1490

0.6114

0.0991

0.7105

7.1680

2000105

0.0026

0.0009

0.0035

3.8540

11

11

2000105

0.0012

0.0009

0.0021

2.3420

0.5121

0.1086

0.6207

5.7180

2005110

0.0011

0.0006

0.0017

2.6750

11

11

2005110

0.0012

0.0006

0.0018

3.1720

0.4300

0.1474

0.5773

3.9170

193512010

0.0016

0.0017

0.0034

1.9300

11

11

193512010

0.0018

0.0019

0.0037

1.9670

0.5840

0.1736

0.7576

4.3640

FF

FF

TABLE!5e:!Equ

al1W


ortfolio!!!!!!!!!+!!!!!!!5x5!Dou

ble1Sort!Test!P

ortfolios!Bu

ilt!Using!Equ

al1W

eighted!Securitie

sCO

MPO

NEN

TS!OF!TH

E!VARIANCE

S!OF!TH

E!!!!!!!!!!!!!(con

t.)

s2(�

2)

s2(�

2)

s2(�

2)

s2(�

3)

s2(�

3)

s2(�

3)

s2(�

2)

s2(�

2)

s2(�

2)

s2(�

3)

s2(�

3)

s2(�

3)

�j,

t

26

4 Conclusion

I extend the calculations of Fama and MacBeth (1973) to include data for 7/1968 through2010. I also reproduce the calculations with 5�5 dual-sorted test portfolios and compare theresults to those with the original 20 beta-sorted portfolios of Fama-MacBeth (1973). In ad-dition, I alternate between the use of a value-weighted and equal-weighted NYSE portfolioas the market portfolio proxy. I also alternate between using equal-weighted and value-weighted averages of underlying security betas and standard deviations of residuals fromsecurity-level market model regressions to construct the corresponding portfolio-level regres-sors for the cross-sectional regression (1).

I find some evidence that the results from Fama-MacBeth (1973) have weakened over time.More importantly I find that using the 5 � 5 test portfolios constructed with a dual-sorton beta and standard deviation of residuals for the underlying securities leads to resultswhich disagree with those from Fama-MacBeth (1973). In particular, I find that the coeffi-cient on the regressor measuring idiosyncratic risk in (1) is significantly different from zerofor testing periods in both 1935-6/1968 (the full sample period of Fama-MacBeth; 1973)and 7/1968-2010. Using some of the other aforementioned variations to the Fama-MacBeth(1973) approach again lead to results inconsistent with those in Fama-MacBeth (1973). Thissuggests that some of the Fama-MacBeth (1973) results may not be robust and casts somedoubt on the relatively good performance of the CAPM12. Overall the results suggest thatadditional robustness inspections would have helped reveal some of the flaws of the CAPMusing the regression specification of Fama-MacBeth (1973) without the need for more ad-vanced statistical tests. More generally, these results hint that for empirical work it maysometimes be important to reproduce the calculations with some variations in the methodused as a means of verifying the robustness of results.

12As mentioned before, this is not a “true” test of the CAPM but rather a test of some practical implicationsof the CAPM conditional on several assumptions.

27

References

[1] Black, Fischer. Capital Market Equilibrium with Restricted Borrowing, Journal of Busi-ness 45 (July 1972): 444-455.

[2] The Center for Research in Security Prices (CRSP).http://www.crsp.com .

[3] Fama, Eugene F. Foundations of Finance, 1976.

[4] Fama, Eugene F.; MacBeth, James D. Risk, Return and Equilibrium: Empirical Tests,Journal of Political Economy, Vol. 81, No. 3 (May - Jun 1973), pp 607-636.

[5] Fama, Eugene F. ; French, KennethMultifactor Explanation of Asset Pricing Anomalies,Journal of Finance, Volume 61, Issue 5, (Oct., 2006).

[6] Fama, Eugene F. ; French, KennethValue Premium and The CAPM, Journal of Finance,Volume 51, Issue 1, (Mar., 1996), 55-84.

[7] French, Kenneth. Fama-French data library.http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data library.html.

[8] Lintner, John. The Valuation of Risk Assets and the Selection of Risky Investments inStock Portfolios and Capital Budgets, Revue of Economics and Statistics 47 (February1965): 13-37.

[9] Sharpe, William F. Capital Asset Prices: A Theory of Market Equilibrium uner Condi-tions of Risk, Journal of Finance 19 (September 1964): 425-442.

28

5 Appendix

Statistics 1 2 3 4 5 6 7 8 9 101 1 1 1 1 1 1 1 1 11

0.2429 0.2938 0.3493 0.5820 0.6477 0.7326 0.7416 0.8639 0.8960 0.89700.1670 0.1910 0.1732 0.0714 0.0597 0.0430 0.0266 0.0098 0.0138 0.02440.5798 0.5798 0.5798 0.5798 0.5798 0.5798 0.5798 0.5798 0.5798 0.57980.0948 0.1058 0.1212 0.1010 0.1085 0.1014 0.1335 0.1080 0.1119 0.13300.0614 0.0645 0.0672 0.0556 0.0476 0.0589 0.0696 0.0587 0.0740 0.07330.0952 0.0952 0.0952 0.0952 0.0952 0.0952 0.0952 0.0904 0.0845 0.08450.6451 0.6775 0.7055 0.5833 0.5000 0.6180 0.7309 0.6493 0.8759 0.8668

1 1 1 1 1 1 1 1 1

0.2668 0.3387 0.6050 0.6437 0.7233 0.7665 0.7711 0.8176 0.8491 1.06000.0752 0.0332 0.0232 0.0204 0.0293 0.0385 0.0280 0.0421 0.0634 0.05120.6756 0.3854 0.4084 0.6536 0.7629 0.7734 0.7550 0.7257 0.7036 0.70410.03682 0.0747 0.0824 0.0442 0.0518 0.0617 0.0617 0.0535 0.0643 0.05910.02097 0.0586 0.0634 0.0260 0.0252 0.0294 0.0306 0.0280 0.0350 0.03220.0481 0.0481 0.0481 0.0481 0.0481 0.0481 0.0481 0.0481 0.0481 0.05470.4359 1.2170 1.3170 0.5403 0.5243 0.6102 0.6349 0.5818 0.7278 0.5885

1 1 1 1 1 1 1 1 1

0.3293 0.3905 0.5648 0.6610 0.7493 0.7529 0.7964 0.8250 0.8816 0.91440.0933 0.1033 0.0503 0.0449 0.0248 0.0378 0.0247 0.0347 0.0180 0.02120.2693 0.5691 0.5072 0.5770 0.5906 0.5423 0.6103 0.6881 0.7282 0.68780.03592 0.0199 0.0318 0.0351 0.0370 0.0405 0.0401 0.0412 0.0408 0.04170.0307 0.0131 0.0223 0.0228 0.0237 0.0274 0.0250 0.0230 0.0213 0.02330.0400 0.0400 0.0400 0.0400 0.0468 0.0400 0.0400 0.0400 0.0400 0.04000.7680 0.3267 0.5585 0.5708 0.5056 0.6860 0.6265 0.5748 0.5321 0.5822

1 1 1 1 1 1 1 1 1

0.3084 0.6031 0.6223 0.7743 0.7955 0.8285 0.8751 0.9072 0.9196 1.00100.0935 0.0887 0.0228 0.0649 0.0625 0.0286 0.0393 0.0451 0.0414 0.02040.7566 0.5757 0.7028 0.5930 0.6010 0.7511 0.7984 0.7489 0.6986 0.54100.03888 0.0383 0.0406 0.0444 0.0511 0.0372 0.0483 0.0478 0.0532 0.05400.01918 0.0250 0.0221 0.0283 0.0323 0.0186 0.0217 0.0239 0.0292 0.03660.0507 0.0507 0.0507 0.0507 0.0507 0.0507 0.0507 0.0507 0.0507 0.05070.3781 0.4921 0.4359 0.5577 0.6360 0.3659 0.4270 0.4716 0.5753 0.7205

1 1 1 1 1 1 1 1 1

0.5577 0.5824 0.6698 0.7220 0.7227 0.7386 0.7784 0.9208 0.9478 0.98250.0696 0.0358 0.0170 0.0291 0.0197 0.0236 0.0381 0.0514 0.0426 0.04350.5299 0.5245 0.5554 0.6317 0.7497 0.6908 0.7312 0.7502 0.6734 0.69040.05095 0.0489 0.0582 0.0508 0.0545 0.0561 0.0594 0.0528 0.0729 0.05210.03493 0.0337 0.0388 0.0309 0.0272 0.0312 0.0308 0.0264 0.0417 0.02900.0559 0.0559 0.0559 0.0559 0.0559 0.0559 0.0559 0.0559 0.0559 0.05590.6244 0.6025 0.6934 0.5515 0.4870 0.5572 0.5507 0.4713 0.7446 0.5179

0.4740 0.5052 0.5535 0.6491 0.7107 0.7495 0.7911 0.8149 0.8261 0.89670.0519 0.0435 0.0219 0.0299 0.0428 0.0361 0.0669 0.0590 0.0475 0.03770.5390 0.6285 0.6055 0.6926 0.4894 0.6959 0.7222 0.6973 0.7140 0.52020.06375 0.0508 0.0474 0.0588 0.0485 0.0670 0.0647 0.0640 0.0725 0.08920.04328 0.0310 0.0298 0.0326 0.0347 0.0370 0.0341 0.0352 0.0388 0.06180.0685 0.0685 0.0685 0.0539 0.0685 0.0685 0.0685 0.0685 0.0685 0.06850.6319 0.4520 0.4346 0.6048 0.5059 0.5398 0.4982 0.5143 0.5662 0.9026

1 1 1 1 1 1 1 1 1

0.5268 0.6173 0.6201 0.6722 0.6926 0.7643 0.8083 0.8420 0.8538 0.88040.0505 0.0429 0.0297 0.0239 0.0508 0.0457 0.0464 0.0413 0.0370 0.02780.3358 0.5076 0.5185 0.5370 0.6284 0.6899 0.6255 0.6965 0.7178 0.58350.04451 0.0318 0.0428 0.0421 0.0414 0.0480 0.0563 0.0471 0.0509 0.05510.03627 0.0223 0.0297 0.0286 0.0253 0.0267 0.0344 0.0260 0.0270 0.03560.0428 0.0428 0.0428 0.0428 0.0428 0.0428 0.0428 0.0540 0.0428 0.04280.8474 0.5204 0.6940 0.6688 0.5900 0.6240 0.8047 0.4807 0.6316 0.8308

1 1 1 1 1 1 1 1 1

0.3647 0.5153 0.5914 0.6054 0.6711 0.8440 0.8632 0.9015 0.9535 0.97440.0689 0.0958 0.0698 0.0611 0.0509 0.0468 0.0325 0.0238 0.0152 0.02260.1919 0.3264 0.4397 0.4914 0.3682 0.4804 0.6637 0.5441 0.5344 0.61330.02505 0.0322 0.0300 0.0340 0.0648 0.0486 0.0446 0.0463 0.0481 0.05690.02252 0.0264 0.0225 0.0242 0.0515 0.0350 0.0259 0.0313 0.0328 0.03540.0347 0.0347 0.0347 0.0347 0.0347 0.0347 0.0347 0.0347 0.0347 0.03470.6483 0.7598 0.6463 0.6979 1.4820 1.0080 0.7442 0.9009 0.9441 1.0180

1 1 1 1 1 1 1 1 1

0.2298 0.2360 0.2894 0.3523 0.7516 0.8021 0.8065 0.8204 0.8401 0.85780.0262 0.0762 0.0705 0.1157 0.0957 0.0800 0.0640 0.0437 0.0681 0.06740.2305 0.1471 0.3252 0.3575 0.4904 0.2743 0.3770 0.5940 0.6077 0.52080.03828 0.0388 0.0394 0.0626 0.0629 0.0611 0.0595 0.0559 0.0507 0.07870.03358 0.0358 0.0324 0.0501 0.0449 0.0520 0.0469 0.0356 0.0317 0.05450.0649 0.0649 0.0649 0.0649 0.0626 0.0626 0.0626 0.0404 0.0626 0.06270.5171 0.5516 0.4983 0.7729 0.7167 0.8308 0.7495 0.8822 0.5066 0.8684

1 1 1 1 1 1 1 1 1

0.2320 0.2843 0.3283 0.4210 0.6107 0.6318 0.6396 0.7380 0.8787 0.92050.0163 0.0848 0.0818 0.0341 0.0122 0.0096 0.0373 0.0525 0.0126 0.01940.3743 0.2956 0.3653 0.4138 0.5038 0.6303 0.2965 0.6764 0.6362 0.68060.03035 0.0254 0.0368 0.0366 0.0510 0.0364 0.0373 0.0447 0.0397 0.04510.024 0.0213 0.0294 0.0280 0.0360 0.0221 0.0313 0.0254 0.0240 0.02550.0450 0.0450 0.0450 0.0450 0.0450 0.0441 0.0450 0.0450 0.0450 0.04410.5340 0.4743 0.6530 0.6235 0.7999 0.5020 0.6963 0.5648 0.5325 0.5775







TABLE12b:1Equal=Weighted1NYSE1Market1Portfolio111111111+1111111201Single=Sort1Test1Portfolios1Built1Using1Value=Weighted1SecuritiesSAMPLE1STATISTICS1FOR1FOUR1SECLECTED1ESTIMATION1PERIODS1(test1portfolios11=10)





�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


1 1 1 1 1 1 1 1 1Statistics 11 12 13 14 15 16 17 18 19 20

1 1 1 1 1 1 1 1 1

0.9502 1.0090 1.0970 1.1640 1.1920 1.2490 1.3510 1.3570 1.3880 1.46100.0283 0.0198 0.0259 0.0530 0.0574 0.0583 0.0591 0.0785 0.0902 0.26830.5798 0.5798 0.5798 0.5798 0.5798 0.5798 0.5798 0.5798 0.5798 0.57980.1506 0.1306 0.1169 0.1360 0.1494 0.1237 0.1413 0.1335 0.1096 0.14540.0815 0.0657 0.0647 0.0815 0.0751 0.0644 0.0789 0.0606 0.0525 0.07050.0904 0.0904 0.0845 0.0904 0.0845 0.0904 0.0845 0.0845 0.0845 0.08450.9011 0.7266 0.7652 0.9010 0.8884 0.7125 0.9334 0.7175 0.6208 0.8336

1 1 1 1 1 1 1 1 1

1.0670 1.1130 1.2400 1.2900 1.2930 1.3230 1.3280 1.3300 1.4310 1.44000.0481 0.0437 0.0679 0.0458 0.0448 0.0533 0.0295 0.0592 0.0620 0.25540.7311 0.6581 0.6973 0.6882 0.7027 0.7055 0.6147 0.6351 0.7762 0.53980.0713 0.0890 0.0963 0.1009 0.0817 0.0844 0.1011 0.0928 0.0806 0.14750.0370 0.0520 0.0530 0.0564 0.0446 0.0458 0.0628 0.0561 0.0381 0.10000.0481 0.0547 0.0481 0.0481 0.0547 0.0547 0.0547 0.0547 0.0547 0.05470.7686 0.9518 1.1020 1.1710 0.8152 0.8380 1.1490 1.0260 0.6978 1.8300

1 1 1 1 1 1 1 1 1

0.9179 1.0770 1.1510 1.1910 1.2020 1.3690 1.3940 1.5160 1.5820 2.08400.0330 0.0480 0.0627 0.0505 0.0290 0.0610 0.0586 0.0732 0.0475 0.20090.6580 0.7794 0.6666 0.5686 0.5103 0.6591 0.7141 0.3799 0.7965 0.57640.0491 0.0484 0.0538 0.0527 0.0486 0.0552 0.0674 0.0738 0.0592 0.07330.0287 0.0227 0.0311 0.0346 0.0340 0.0322 0.0361 0.0581 0.0267 0.04770.0468 0.0400 0.0400 0.0468 0.0468 0.0468 0.0400 0.0468 0.0468 0.04680.6133 0.5689 0.7768 0.7392 0.7264 0.6889 0.9017 1.2420 0.5702 1.0200

1 1 1 1 1 1 1 1 1

1.0540 1.0870 1.1440 1.1820 1.1870 1.2580 1.2670 1.4850 1.5260 1.88400.0190 0.0518 0.0531 0.0577 0.0525 0.0520 0.0286 0.0536 0.0590 0.16690.7913 0.6931 0.6910 0.7351 0.7024 0.7319 0.6285 0.7422 0.5808 0.65970.0586 0.0543 0.0593 0.0569 0.0642 0.0589 0.0603 0.0711 0.0549 0.06120.0268 0.0301 0.0330 0.0293 0.0350 0.0305 0.0368 0.0361 0.0356 0.03570.0507 0.0582 0.0582 0.0507 0.0580 0.0582 0.0582 0.0580 0.0580 0.05800.5276 0.5167 0.5661 0.5774 0.6036 0.5238 0.6315 0.6218 0.6128 0.6151

1 1 1 1 1 1 1 1 1

0.9893 0.9974 1.0170 1.0190 1.0270 1.0620 1.0660 1.0900 1.3280 1.41800.0467 0.0509 0.0510 0.0595 0.0661 0.0736 0.0811 0.1053 0.0857 0.06570.6304 0.8520 0.8041 0.8538 0.6594 0.7420 0.6875 0.8346 0.8022 0.67900.0678 0.0610 0.0651 0.0700 0.0545 0.0764 0.0795 0.0730 0.0681 0.07190.0412 0.0235 0.0288 0.0268 0.0318 0.0388 0.0445 0.0297 0.0303 0.04070.0559 0.0653 0.0653 0.0559 0.0653 0.0653 0.0653 0.0650 0.0653 0.06500.7370 0.3597 0.4413 0.4783 0.4870 0.5948 0.6812 0.4567 0.4638 0.6265

0.9119 0.9925 1.0040 1.0240 1.0240 1.2080 1.2240 1.3400 1.3450 1.45400.0395 0.0809 0.0810 0.0628 0.0561 0.0604 0.0711 0.1002 0.1040 0.02160.7724 0.7283 0.8525 0.7324 0.7033 0.7958 0.8480 0.6657 0.7276 0.74050.0735 0.0665 0.0850 0.0889 0.0743 0.0970 0.0790 0.0931 0.0969 0.08760.0351 0.0346 0.0326 0.0460 0.0405 0.0439 0.0308 0.0538 0.0506 0.04460.0685 0.0539 0.0685 0.0539 0.0539 0.0539 0.0539 0.0685 0.0539 0.05390.5117 0.6423 0.4765 0.8522 0.7507 0.8129 0.5706 0.7857 0.9372 0.8274

1 1 1 1 1 1 1 1 1

0.9455 0.9898 1.0030 1.0380 1.0530 1.1030 1.1120 1.1870 1.2690 1.56800.0393 0.0139 0.0175 0.0304 0.0245 0.0353 0.0428 0.0501 0.1090 0.06140.7385 0.6304 0.6533 0.7723 0.5250 0.6694 0.7144 0.6682 0.4629 0.51320.0590 0.0532 0.0511 0.0583 0.0687 0.0499 0.0650 0.0610 0.0821 0.09110.0302 0.0324 0.0301 0.0278 0.0473 0.0287 0.0348 0.0352 0.0602 0.06350.0428 0.0540 0.0540 0.0540 0.0540 0.0540 0.0428 0.0428 0.0540 0.05400.7046 0.5994 0.5573 0.5148 0.8764 0.5321 0.8119 0.8213 1.1140 1.1770

1 1 1 1 1 1 1 1 1

0.9746 0.9797 1.0500 1.0740 1.1180 1.1300 1.1470 1.1680 1.2400 1.24600.0273 0.0361 0.0242 0.0355 0.0179 0.0274 0.0383 0.0474 0.1104 0.13100.5765 0.5451 0.5824 0.6045 0.1389 0.4995 0.5808 0.2737 0.5450 0.37720.0655 0.0692 0.0558 0.0637 0.0508 0.0714 0.0668 0.1207 0.0778 0.08750.0426 0.0467 0.0360 0.0400 0.0472 0.0505 0.0433 0.1028 0.0525 0.06910.0347 0.0347 0.0444 0.0444 0.0444 0.0444 0.0444 0.0444 0.0444 0.04441.2260 1.3440 0.8124 0.9024 1.0630 1.1380 0.9754 2.3190 1.1830 1.5570

1 1 1 1 1 1 1 1 1

0.9436 1.0240 1.0780 1.2360 1.2750 1.2820 1.3020 1.4220 1.4300 1.67000.0573 0.0461 0.0331 0.0776 0.0684 0.0426 0.0533 0.0780 0.0968 0.22040.5525 0.5833 0.5839 0.4964 0.6446 0.6085 0.6742 0.6555 0.6070 0.57820.0595 0.0603 0.0710 0.0652 0.0940 0.1102 0.0863 0.0827 0.0938 0.10170.0398 0.0389 0.0458 0.0463 0.0560 0.0689 0.0493 0.0486 0.0588 0.06610.0627 0.0628 0.0404 0.0404 0.0404 0.0628 0.0404 0.0404 0.0404 0.04040.6347 0.6192 1.1350 1.1460 1.3880 1.0970 1.2200 1.2030 1.4570 1.6360

1 1 1 1 1 1 1 1 1

0.9931 1.0500 1.0870 1.1060 1.1490 1.2170 1.2770 1.3360 1.3710 1.42900.0203 0.0197 0.0163 0.0351 0.0223 0.0328 0.0158 0.0066 0.0332 0.01820.6425 0.5224 0.6469 0.5710 0.6738 0.7202 0.6638 0.6686 0.6580 0.57990.0394 0.0546 0.0536 0.0493 0.0555 0.0525 0.0583 0.0577 0.0576 0.06450.0236 0.0377 0.0319 0.0323 0.0317 0.0278 0.0338 0.0332 0.0337 0.04180.0450 0.0320 0.0450 0.0320 0.0320 0.0320 0.0320 0.0320 0.0320 0.03200.5232 1.1780 0.7078 1.0090 0.9900 0.8674 1.0550 1.0380 1.0510 1.3070









TABLE12b:1Equal=Weighted1NYSE1Market1Portfolio111111111+1111111201Single=Sort1Test1Portfolios1Built1Using1Value=Weighted1SecuritiesSAMPLE1STATISTICS1FOR1FOUR1SECLECTED1ESTIMATION1PERIODS1(test1portfolios111=20)1111



�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


30

Statistics 1 2 3 4 5 6 7 8 9 101 1 1 1 1 1 1 1 1 11

0.2429 0.2938 0.3493 0.5820 0.6477 0.7326 0.7416 0.8639 0.8960 0.89700.2370 0.3565 0.3356 0.2189 0.1936 0.1798 0.1760 0.1712 0.2201 0.22800.6409 0.6409 0.6409 0.6409 0.6409 0.6409 0.6409 0.6409 0.6409 0.64090.0798 0.1009 0.0935 0.0965 0.1111 0.1023 0.0998 0.1009 0.1010 0.10870.0478 0.0338 0.0363 0.0310 0.0486 0.0486 0.0358 0.0334 0.0374 0.03400.0907 0.0907 0.0907 0.0907 0.0907 0.0907 0.0907 0.0808 0.0808 0.08080.5275 0.3732 0.4005 0.3418 0.5355 0.5359 0.3945 0.4128 0.4624 0.4210

1 1 1 1 1 1 1 1 1

0.5290 0.8304 0.9300 1.0190 1.0480 1.1270 1.3160 1.4110 1.4840 1.50500.0163 0.0157 0.0289 0.0314 0.0060 0.0208 0.0157 0.0229 0.0350 0.03590.5719 0.7561 0.8473 0.9053 0.9344 0.8725 0.8049 0.8533 0.6512 0.70620.03975 0.0499 0.0427 0.0435 0.0440 0.0486 0.0575 0.0596 0.0630 0.06880.02601 0.0246 0.0167 0.0134 0.0113 0.0173 0.0254 0.0228 0.0372 0.03730.0541 0.0541 0.0544 0.0541 0.0544 0.0544 0.0544 0.0544 0.0544 0.05440.4811 0.4555 0.3068 0.2476 0.2070 0.3186 0.4664 0.4191 0.6835 0.6851

1 1 1 1 1 1 1 1 1

0.6639 0.8237 0.8852 0.8949 1.0530 1.0570 1.0720 1.1230 1.1680 1.28700.0189 0.0409 0.0382 0.0168 0.0474 0.0114 0.0054 0.0204 0.0191 0.04360.6283 0.7373 0.7789 0.8566 0.8291 0.9115 0.9055 0.8451 0.8364 0.87620.02298 0.0251 0.0232 0.0274 0.0338 0.0331 0.0368 0.0333 0.0393 0.03630.01401 0.0129 0.0109 0.0104 0.0140 0.0098 0.0113 0.0131 0.0159 0.01280.0404 0.0404 0.0404 0.0404 0.0404 0.0404 0.0404 0.0404 0.0404 0.04040.3469 0.3186 0.2697 0.2565 0.3461 0.2435 0.2800 0.3240 0.3932 0.3163

1 1 1 1 1 1 1 1 1

0.4917 0.5419 0.7179 0.7376 0.7852 0.8959 0.9459 0.9474 0.9681 0.98980.0375 0.0237 0.0818 0.0306 0.0307 0.0523 0.0614 0.0235 0.0301 0.03330.7813 0.8043 0.8517 0.8915 0.8830 0.7752 0.8350 0.8133 0.8059 0.84380.03373 0.0341 0.0345 0.0359 0.0374 0.0408 0.0410 0.0398 0.0441 0.04490.01577 0.0151 0.0133 0.0118 0.0128 0.0193 0.0167 0.0172 0.0194 0.01770.0552 0.0552 0.0552 0.0552 0.0552 0.0552 0.0552 0.0506 0.0552 0.05060.2859 0.2732 0.2406 0.2140 0.2320 0.3505 0.3017 0.3401 0.3521 0.3505

1 1 1 1 1 1 1 1 1

0.6953 0.7497 0.8465 0.8541 0.8703 0.9791 1.0060 1.0150 1.0440 1.08700.0312 0.0240 0.0117 0.0236 0.0172 0.0279 0.0238 0.0226 0.0240 0.02950.7238 0.7875 0.7877 0.8072 0.8487 0.8646 0.8814 0.8217 0.8696 0.80920.04368 0.0407 0.0436 0.0469 0.0486 0.0453 0.0517 0.0578 0.0509 0.06140.02295 0.0187 0.0201 0.0206 0.0189 0.0167 0.0178 0.0244 0.0184 0.02680.0759 0.0759 0.0759 0.0759 0.0759 0.0759 0.0759 0.0759 0.0759 0.05730.3025 0.2470 0.2649 0.2714 0.2491 0.2199 0.2348 0.3216 0.2420 0.4676

0.7939 0.8983 0.9204 0.9619 0.9936 0.9944 1.0360 1.1140 1.1540 1.22400.0702 0.0546 0.0219 0.0197 0.0279 0.0153 0.0136 0.0259 0.0352 0.04410.5474 0.6395 0.7570 0.7154 0.7896 0.7917 0.8052 0.8313 0.8506 0.87440.05356 0.0520 0.0461 0.0499 0.0511 0.0559 0.0525 0.0579 0.0609 0.05580.03603 0.0312 0.0228 0.0266 0.0234 0.0255 0.0232 0.0238 0.0236 0.01980.0694 0.0694 0.0694 0.0694 0.0694 0.0694 0.0694 0.0694 0.0694 0.05730.5189 0.4497 0.3276 0.3833 0.3372 0.3672 0.3339 0.3425 0.3393 0.3453

1 1 1 1 1 1 1 1 1

0.6761 0.7001 0.8386 0.8839 0.9171 0.9599 1.0020 1.0170 1.0250 1.08100.0193 0.0255 0.0483 0.0540 0.0079 0.0131 0.0110 0.0098 0.0094 0.01410.6736 0.6442 0.8487 0.8661 0.8926 0.8462 0.8583 0.8888 0.8850 0.82390.02831 0.0300 0.0360 0.0390 0.0395 0.0389 0.0403 0.0422 0.0486 0.04700.01618 0.0179 0.0140 0.0143 0.0129 0.0152 0.0152 0.0141 0.0165 0.01970.0448 0.0448 0.0448 0.0448 0.0448 0.0448 0.0448 0.0448 0.0448 0.05350.3609 0.3986 0.3125 0.3181 0.2885 0.3401 0.3387 0.3140 0.3679 0.3693

1 1 1 1 1 1 1 1 1

0.4389 0.5208 0.6935 0.7940 0.7989 0.9664 1.0210 1.0260 1.0530 1.07900.0143 0.0162 0.0485 0.0082 0.0606 0.0215 0.0041 0.0034 0.0082 0.01380.5295 0.5258 0.6500 0.7772 0.6086 0.7697 0.8501 0.8392 0.6635 0.62610.02586 0.0299 0.0287 0.0337 0.0369 0.0410 0.0421 0.0393 0.0438 0.04810.01774 0.0206 0.0170 0.0159 0.0231 0.0197 0.0163 0.0158 0.0254 0.02940.0498 0.0498 0.0498 0.0498 0.0498 0.0498 0.0498 0.0458 0.0458 0.04580.3565 0.4143 0.3414 0.3200 0.4637 0.3950 0.3275 0.3437 0.5541 0.6422

1 1 1 1 1 1 1 1 1

0.3921 0.4585 0.5013 0.6583 0.7675 0.8564 0.8583 0.8936 0.9670 0.97970.0616 0.0631 0.0438 0.0728 0.0173 0.0352 0.0414 0.0394 0.0518 0.04580.0895 0.1464 0.1993 0.3379 0.5999 0.7332 0.5816 0.6168 0.6026 0.72630.01992 0.0298 0.0371 0.0453 0.0485 0.0432 0.0455 0.0461 0.0466 0.05230.01901 0.0275 0.0332 0.0369 0.0307 0.0223 0.0294 0.0285 0.0294 0.02730.1023 0.1023 0.1032 0.1007 0.1020 0.1010 0.1010 0.1013 0.0982 0.09840.1859 0.2690 0.3212 0.3665 0.3008 0.2208 0.2912 0.2817 0.2988 0.2779

1 1 1 1 1 1 1 1 1

0.2320 0.2843 0.3283 0.4210 0.6107 0.6318 0.6396 0.7380 0.8787 0.92050.0123 0.0144 0.0352 0.0156 0.0672 0.0522 0.0495 0.0367 0.0371 0.03810.2621 0.3597 0.3541 0.5611 0.6257 0.6987 0.6983 0.6988 0.7286 0.77240.03163 0.0246 0.0305 0.0297 0.0368 0.0341 0.0328 0.0326 0.0371 0.03950.02717 0.0197 0.0245 0.0197 0.0225 0.0187 0.0180 0.0179 0.0193 0.01880.0542 0.0542 0.0542 0.0542 0.0541 0.0541 0.0545 0.0545 0.0545 0.05450.5011 0.3630 0.4517 0.3624 0.4154 0.3456 0.3304 0.3277 0.3542 0.3458







TABLE12c:1Value=Weighted1NYSE1Market1Portfolio111111111+1111111201Single=Sort1Test1Portfolios1Built1Using1Equal=Weighted1SecuritiesSAMPLE1STATISTICS1FOR1FOUR1SECLECTED1ESTIMATION1PERIODS1(test1portfolios11=10)





�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


31

1 1 1 1 1 1 1 1 1Statistics 11 12 13 14 15 16 17 18 19 20

1 1 1 1 1 1 1 1 1

0.9502 1.0090 1.0970 1.1640 1.1920 1.2490 1.3510 1.3570 1.3880 1.46100.2397 0.2268 0.2138 0.2025 0.1905 0.2091 0.2051 0.1946 0.1897 0.23460.6409 0.6409 0.6409 0.6409 0.6409 0.6409 0.6409 0.6409 0.6409 0.64090.1162 0.1178 0.1176 0.1185 0.0998 0.1169 0.1231 0.1178 0.1265 0.12920.0427 0.0335 0.0486 0.0459 0.0353 0.0389 0.0525 0.0392 0.0406 0.04130.0808 0.0878 0.0878 0.0808 0.0878 0.0878 0.0878 0.0878 0.0878 0.08780.5286 0.3815 0.5536 0.5673 0.4025 0.4428 0.5976 0.4467 0.4626 0.4705

1 1 1 1 1 1 1 1 1

1.5420 1.5720 1.5930 1.6850 1.8110 1.9060 1.9210 1.9700 2.0320 2.11600.0194 0.0238 0.0178 0.0177 0.0587 0.0397 0.0213 0.0307 0.0208 0.04890.7189 0.7290 0.7719 0.6975 0.7670 0.5981 0.7052 0.6380 0.5798 0.61150.0686 0.0672 0.0670 0.0701 0.0715 0.0871 0.0793 0.1008 0.0986 0.10590.0363 0.0350 0.0320 0.0385 0.0345 0.0552 0.0430 0.0607 0.0639 0.06600.0544 0.0544 0.0561 0.0561 0.0561 0.0561 0.0561 0.0561 0.0561 0.05610.6676 0.6431 0.5708 0.6874 0.6158 0.9848 0.7675 1.0820 1.1400 1.1770

1 1 1 1 1 1 1 1 1

1.3320 1.3520 1.4090 1.4290 1.5350 1.7040 1.7040 1.7510 1.8230 1.85700.0538 0.0427 0.0580 0.0442 0.0694 0.0983 0.0870 0.0725 0.0921 0.09310.8244 0.8385 0.7454 0.7816 0.7566 0.8506 0.7901 0.6184 0.7302 0.57700.0392 0.0402 0.0414 0.0437 0.0466 0.0479 0.0490 0.0532 0.0549 0.05650.0164 0.0162 0.0209 0.0204 0.0230 0.0185 0.0224 0.0329 0.0285 0.03680.0404 0.0443 0.0443 0.0443 0.0404 0.0443 0.0443 0.0443 0.0443 0.04430.4065 0.3649 0.4717 0.4615 0.5688 0.4187 0.5066 0.7426 0.6435 0.8304

1 1 1 1 1 1 1 1 1

1.0560 1.0640 1.0750 1.0910 1.1180 1.1340 1.1370 1.1620 1.2450 1.33100.0398 0.0314 0.0132 0.0144 0.0164 0.0162 0.0127 0.0228 0.0190 0.02980.8210 0.8637 0.8030 0.8316 0.8103 0.8010 0.7964 0.8149 0.7631 0.73740.0439 0.0449 0.0481 0.0473 0.0476 0.0466 0.0482 0.0516 0.0579 0.05630.0186 0.0166 0.0213 0.0194 0.0207 0.0208 0.0218 0.0222 0.0282 0.02880.0552 0.0506 0.0552 0.0506 0.0506 0.0552 0.0552 0.0506 0.0506 0.05060.3366 0.3276 0.3868 0.3838 0.4093 0.3763 0.3943 0.4389 0.5573 0.5697

1 1 1 1 1 1 1 1 1

1.1040 1.1160 1.1250 1.1530 1.1540 1.1610 1.2220 1.3100 1.3270 1.40900.0294 0.0268 0.0300 0.0318 0.0375 0.0399 0.0319 0.0491 0.0562 0.05150.8662 0.8317 0.8716 0.8280 0.8959 0.8700 0.8485 0.8515 0.8464 0.82680.0568 0.0532 0.0548 0.0576 0.0589 0.0590 0.0586 0.0593 0.0663 0.06260.0208 0.0218 0.0196 0.0239 0.0190 0.0213 0.0228 0.0229 0.0260 0.02610.0759 0.0759 0.0573 0.0573 0.0759 0.0573 0.0573 0.0573 0.0563 0.05630.2739 0.2878 0.3424 0.4169 0.2505 0.3711 0.3981 0.3987 0.4622 0.4630

1.2600 1.2830 1.2890 1.3010 1.3180 1.3650 1.4250 1.4570 1.6480 1.75200.0537 0.0588 0.0524 0.0536 0.0389 0.0469 0.0519 0.0541 0.0916 0.09330.7906 0.7829 0.7752 0.8239 0.7682 0.7988 0.7861 0.7491 0.6596 0.66570.0675 0.0671 0.0660 0.0673 0.0689 0.0755 0.0723 0.0773 0.0850 0.09480.0309 0.0313 0.0313 0.0282 0.0332 0.0339 0.0334 0.0387 0.0496 0.05480.0694 0.0694 0.0694 0.0573 0.0573 0.0573 0.0573 0.0573 0.0573 0.05730.4450 0.4501 0.4509 0.4932 0.5794 0.5913 0.5835 0.6763 0.8659 0.9571

1 1 1 1 1 1 1 1 1

1.1030 1.1170 1.1270 1.1660 1.2140 1.2200 1.2730 1.3260 1.3600 1.55800.0140 0.0084 0.0069 0.0184 0.0129 0.0100 0.0158 0.0265 0.0355 0.02190.8952 0.8975 0.8460 0.8246 0.8718 0.8138 0.7459 0.7626 0.8038 0.75330.0483 0.0450 0.0469 0.0483 0.0479 0.0508 0.0521 0.0513 0.0578 0.06070.0156 0.0144 0.0184 0.0202 0.0172 0.0219 0.0263 0.0250 0.0256 0.03020.0448 0.0535 0.0448 0.0448 0.0535 0.0535 0.0535 0.0535 0.0535 0.05350.3487 0.2696 0.4110 0.4511 0.3210 0.4103 0.4913 0.4675 0.4786 0.5643

1 1 1 1 1 1 1 1 1

1.1070 1.1140 1.1210 1.1240 1.1800 1.1870 1.2320 1.2380 1.2570 1.31000.0239 0.0225 0.0231 0.0088 0.0150 0.0143 0.0244 0.0199 0.0288 0.02700.7705 0.7266 0.6294 0.6039 0.1712 0.7101 0.5851 0.6291 0.5460 0.48560.0415 0.0456 0.0478 0.0489 0.0587 0.0488 0.0499 0.0528 0.0548 0.06750.0199 0.0239 0.0291 0.0308 0.0534 0.0263 0.0322 0.0322 0.0369 0.04840.0458 0.0458 0.0458 0.0458 0.0444 0.0458 0.0444 0.0444 0.0444 0.04440.4333 0.5205 0.6350 0.6724 1.2030 0.5734 0.7244 0.7241 0.8312 1.0900

1 1 1 1 1 1 1 1 1

0.9868 0.9912 1.0120 1.0800 1.1630 1.1800 1.2010 1.2270 1.2410 1.42800.0370 0.0210 0.0259 0.0357 0.0500 0.0486 0.0480 0.0466 0.0123 0.03390.7317 0.6747 0.6446 0.6843 0.6848 0.6764 0.6974 0.6340 0.6353 0.67580.0539 0.0472 0.0586 0.0624 0.0720 0.0659 0.0620 0.0654 0.0734 0.08040.0279 0.0269 0.0350 0.0351 0.0404 0.0375 0.0341 0.0396 0.0443 0.04580.1014 0.0594 0.0594 0.1014 0.0594 0.0580 0.0588 0.0588 0.0588 0.05880.2754 0.4537 0.5886 0.3456 0.6810 0.6466 0.5794 0.6723 0.7532 0.7780

1 1 1 1 1 1 1 1 1

0.9931 1.0500 1.0870 1.1060 1.1490 1.2170 1.2770 1.3360 1.3710 1.42900.0393 0.0522 0.0646 0.0454 0.0605 0.0637 0.0977 0.1123 0.0587 0.05440.8442 0.7029 0.7349 0.8028 0.8241 0.7042 0.7414 0.8081 0.7778 0.77950.0421 0.0379 0.0400 0.0413 0.0449 0.0459 0.0441 0.0473 0.0487 0.05640.0166 0.0207 0.0206 0.0184 0.0188 0.0250 0.0224 0.0207 0.0229 0.02650.0533 0.0533 0.0409 0.0411 0.0405 0.0405 0.0405 0.0405 0.0405 0.04040.3118 0.3881 0.5033 0.4466 0.4645 0.6154 0.5536 0.5105 0.5657 0.6560









TABLE12c:1Value=Weighted1NYSE1Market1Portfolio111111111+1111111201Single=Sort1Test1Portfolios1Built1Using1Equal=Weighted1SecuritiesSAMPLE1STATISTICS1FOR1FOUR1SECLECTED1ESTIMATION1PERIODS1(test1portfolios111=20)111



�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


32

Statistics 1 2 3 4 5 6 7 8 9 101 1 1 1 1 1 1 1 1 11

0.2429 0.2938 0.3493 0.5820 0.6477 0.7326 0.7416 0.8639 0.8960 0.89700.1763 0.2919 0.2994 0.1914 0.1908 0.2014 0.1780 0.1756 0.1832 0.18940.5475 0.5475 0.5475 0.5475 0.5475 0.5475 0.5475 0.5475 0.5475 0.54750.0949 0.1112 0.1055 0.1161 0.1185 0.1106 0.1249 0.1148 0.1134 0.13140.0638 0.0703 0.0702 0.0585 0.0654 0.0735 0.0754 0.0613 0.0720 0.07610.1152 0.1152 0.1152 0.1152 0.1152 0.1089 0.1152 0.1152 0.0885 0.10890.5542 0.6105 0.6093 0.5078 0.5675 0.6754 0.6545 0.5319 0.8136 0.6995

1 1 1 1 1 1 1 1 1

0.6907 0.7579 0.7992 1.0160 1.0280 1.2490 1.2990 1.3500 1.4260 1.44500.1303 0.0402 0.0315 0.0708 0.0724 0.0813 0.0550 0.0562 0.0552 0.05730.3996 0.3970 0.5800 0.6321 0.6258 0.7861 0.6356 0.7520 0.5351 0.51310.04332 0.0821 0.0512 0.0507 0.0582 0.0521 0.0612 0.0615 0.0649 0.07410.03357 0.0637 0.0332 0.0307 0.0356 0.0241 0.0369 0.0306 0.0443 0.05170.0464 0.0464 0.0464 0.0464 0.0464 0.0464 0.0464 0.0464 0.0464 0.04640.7241 1.3750 0.7157 0.6627 0.7679 0.5200 0.7964 0.6607 0.9546 1.1150

1 1 1 1 1 1 1 1 1

0.4036 0.7557 0.8834 0.9378 0.9882 1.0020 1.1100 1.1270 1.2070 1.29200.0895 0.0883 0.0503 0.0496 0.0606 0.0154 0.0395 0.0317 0.0464 0.06430.3093 0.4507 0.5238 0.6160 0.6631 0.7381 0.4884 0.5486 0.6369 0.67710.03506 0.0251 0.0276 0.0337 0.0420 0.0402 0.0407 0.0377 0.0457 0.04110.02914 0.0186 0.0191 0.0209 0.0244 0.0206 0.0291 0.0253 0.0276 0.02340.0451 0.0451 0.0451 0.0451 0.0451 0.0479 0.0451 0.0478 0.0451 0.04510.6460 0.4125 0.4229 0.4635 0.5405 0.4295 0.6450 0.5295 0.6108 0.5178

1 1 1 1 1 1 1 1 1

0.3692 0.5439 0.5548 0.7022 0.7401 0.8784 0.8991 1.0010 1.0080 1.00900.1063 0.0407 0.0326 0.0502 0.0137 0.0503 0.0571 0.0809 0.0702 0.06670.6838 0.6043 0.6176 0.7301 0.5911 0.5519 0.6817 0.6059 0.5960 0.66540.04185 0.0384 0.0476 0.0361 0.0429 0.0531 0.0497 0.0468 0.0518 0.05770.02353 0.0241 0.0295 0.0187 0.0274 0.0356 0.0281 0.0294 0.0329 0.03340.0581 0.0581 0.0581 0.0581 0.0581 0.0581 0.0581 0.0552 0.0552 0.05810.4049 0.4151 0.5067 0.3224 0.4716 0.6120 0.4828 0.5319 0.5959 0.5744

1 1 1 1 1 1 1 1 1

0.5734 0.6521 0.8431 0.8757 0.9168 0.9565 1.0080 1.0220 1.0260 1.06400.0729 0.0538 0.0282 0.0258 0.0423 0.0444 0.0307 0.0242 0.0257 0.01480.6108 0.5302 0.5707 0.6686 0.6316 0.7285 0.6185 0.5459 0.7113 0.54690.05569 0.0586 0.0525 0.0535 0.0586 0.0535 0.0573 0.0690 0.0642 0.06660.03474 0.0402 0.0344 0.0308 0.0356 0.0279 0.0354 0.0465 0.0345 0.04490.0719 0.0719 0.0719 0.0719 0.0719 0.0719 0.0719 0.0719 0.0719 0.07190.4834 0.5589 0.4787 0.4288 0.4948 0.3880 0.4928 0.6465 0.4801 0.6241

0.6564 0.8040 0.8971 0.9254 0.9677 1.0400 1.0690 1.0930 1.1270 1.20200.0315 0.0666 0.0343 0.0320 0.0310 0.0248 0.0289 0.0322 0.0423 0.04780.3181 0.5747 0.6134 0.5198 0.5941 0.5150 0.6161 0.7174 0.6042 0.62100.0696 0.0525 0.0467 0.0610 0.0590 0.0738 0.0544 0.0631 0.0907 0.08200.05748 0.0342 0.0291 0.0422 0.0376 0.0514 0.0337 0.0336 0.0571 0.05050.0599 0.0599 0.0599 0.0599 0.0599 0.0599 0.0599 0.0696 0.0599 0.06960.9600 0.5713 0.4854 0.7056 0.6281 0.8583 0.5628 0.4820 0.9536 0.7250

1 1 1 1 1 1 1 1 1

0.7104 0.7611 0.8536 0.9193 0.9682 0.9778 0.9893 0.9980 1.0020 1.08700.0640 0.0253 0.0496 0.0351 0.0674 0.0401 0.0479 0.0493 0.0406 0.04030.3757 0.3402 0.6337 0.7240 0.6013 0.6164 0.6932 0.7031 0.5678 0.55820.04095 0.0355 0.0416 0.0443 0.0531 0.0473 0.0455 0.0528 0.0527 0.05790.03235 0.0289 0.0252 0.0233 0.0335 0.0293 0.0252 0.0288 0.0346 0.03850.0391 0.0391 0.0391 0.0391 0.0391 0.0391 0.0391 0.0391 0.0570 0.03910.8271 0.7378 0.6439 0.5953 0.8565 0.7492 0.6437 0.7360 0.6072 0.9832

1 1 1 1 1 1 1 1 1

0.4015 0.5794 0.6091 0.7069 0.8113 0.8413 0.9452 0.9677 0.9770 1.06700.0503 0.0706 0.0689 0.0345 0.0899 0.0849 0.0746 0.0337 0.0443 0.01660.3030 0.4550 0.5382 0.5049 0.2510 0.4264 0.6303 0.6387 0.5314 0.49920.02638 0.0338 0.0281 0.0377 0.0517 0.0578 0.0484 0.0456 0.0539 0.05890.02202 0.0250 0.0191 0.0265 0.0447 0.0438 0.0294 0.0274 0.0369 0.04170.0429 0.0429 0.0429 0.0429 0.0355 0.0429 0.0429 0.0429 0.0355 0.04630.5133 0.5823 0.4454 0.6180 1.2580 1.0210 0.6853 0.6382 1.0370 0.9003

1 1 1 1 1 1 1 1 1

0.3242 0.3928 0.4614 0.5923 0.6126 0.6610 0.7742 0.7779 0.8698 0.97860.0656 0.0437 0.0528 0.0403 0.0699 0.0475 0.0498 0.0505 0.0185 0.04280.1058 0.1889 0.1453 0.2601 0.3717 0.4622 0.3615 0.4389 0.3134 0.41840.03297 0.0430 0.0618 0.0529 0.0707 0.0577 0.0493 0.0571 0.0668 0.06200.03117 0.0387 0.0571 0.0455 0.0561 0.0423 0.0394 0.0428 0.0554 0.04730.0858 0.0822 0.0853 0.0853 0.0740 0.0856 0.0823 0.0823 0.0765 0.08210.3635 0.4710 0.6698 0.5333 0.7578 0.4944 0.4791 0.5200 0.7235 0.5759

1 1 1 1 1 1 1 1 1

0.2320 0.2843 0.3283 0.4210 0.6107 0.6318 0.6396 0.7380 0.8787 0.92050.0374 0.0307 0.0117 0.0513 0.0331 0.0028 0.1039 0.0671 0.0170 0.01610.1926 0.2473 0.2113 0.4225 0.4154 0.5501 0.4451 0.3997 0.3470 0.43850.03871 0.0301 0.0385 0.0339 0.0420 0.0479 0.0342 0.0393 0.0424 0.04750.03478 0.0261 0.0342 0.0257 0.0321 0.0321 0.0255 0.0304 0.0343 0.03560.0460 0.0460 0.0460 0.0460 0.0460 0.0460 0.0461 0.0452 0.0443 0.04610.7557 0.5672 0.7433 0.5594 0.6978 0.6985 0.5533 0.6737 0.7748 0.7723







TABLE12d:1Value=Weighted1NYSE1Market1Portfolio111111111+1111111201Single=Sort1Test1Portfolios1Built1Using1Value=Weighted1SecuritiesSAMPLE1STATISTICS1FOR1FOUR1SECLECTED1ESTIMATION1PERIODS1(test1portfolios11=10)





�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


33

1 1 1 1 1 1 1 1 1Statistics 11 12 13 14 15 16 17 18 19 20

1 1 1 1 1 1 1 1 1

0.9502 1.0090 1.0970 1.1640 1.1920 1.2490 1.3510 1.3570 1.3880 1.46100.2156 0.2127 0.2058 0.2172 0.2292 0.2414 0.2177 0.3308 0.4062 0.85380.5475 0.5475 0.5475 0.5475 0.5475 0.5475 0.5475 0.5475 0.5475 0.54750.1413 0.1210 0.1227 0.1207 0.1011 0.1544 0.1149 0.1235 0.1222 0.13870.0728 0.0618 0.0559 0.0668 0.0475 0.0939 0.0625 0.0605 0.0660 0.06750.0885 0.1089 0.1089 0.0885 0.0885 0.0885 0.0885 0.1089 0.0885 0.08850.8228 0.5677 0.5137 0.7550 0.5373 1.0620 0.7064 0.5554 0.7457 0.7631

1 1 1 1 1 1 1 1 1

1.4870 1.6080 1.6980 1.7210 1.7550 1.7680 1.7910 1.8160 2.0810 2.15700.0405 0.0350 0.0461 0.0501 0.0667 0.0754 0.0609 0.0876 0.0630 0.09870.3442 0.3915 0.4504 0.6082 0.5329 0.5017 0.4693 0.4700 0.6505 0.35420.0944 0.0753 0.0873 0.0833 0.0687 0.0900 0.0963 0.1029 0.0878 0.13610.0764 0.0587 0.0647 0.0521 0.0470 0.0635 0.0702 0.0750 0.0519 0.10940.0464 0.0541 0.0541 0.0464 0.0541 0.0541 0.0541 0.0541 0.0541 0.05411.6490 1.0870 1.1980 1.1240 0.8686 1.1750 1.2980 1.3870 0.9599 2.0230

1 1 1 1 1 1 1 1 1

1.3050 1.3490 1.4580 1.4820 1.6730 1.7020 1.7910 1.8840 1.8900 1.96600.0313 0.0323 0.0629 0.0708 0.1028 0.1077 0.1271 0.1505 0.1305 0.07420.6004 0.7015 0.4378 0.6820 0.5855 0.6008 0.3641 0.3005 0.5035 0.43070.0422 0.0453 0.0488 0.0568 0.0556 0.0544 0.0691 0.0679 0.0580 0.06680.0267 0.0247 0.0366 0.0320 0.0358 0.0344 0.0551 0.0568 0.0409 0.05040.0451 0.0451 0.0478 0.0451 0.0479 0.0478 0.0478 0.0451 0.0478 0.04790.5919 0.5483 0.7649 0.7101 0.7476 0.7181 1.1520 1.2580 0.8539 1.0530

1 1 1 1 1 1 1 1 1

1.0180 1.0280 1.0330 1.0440 1.0800 1.1530 1.3170 1.3390 1.4220 1.61700.0452 0.0528 0.0474 0.0529 0.0480 0.0468 0.0559 0.0554 0.0802 0.14040.5765 0.6170 0.6668 0.6704 0.6153 0.4737 0.6798 0.6021 0.5173 0.56060.0594 0.0517 0.0555 0.0611 0.0535 0.0725 0.0479 0.0622 0.0608 0.06350.0387 0.0320 0.0321 0.0351 0.0332 0.0526 0.0271 0.0392 0.0422 0.04210.0552 0.0581 0.0552 0.0581 0.0581 0.0581 0.0552 0.0552 0.0552 0.05520.6999 0.5508 0.5803 0.6033 0.5709 0.9045 0.4907 0.7099 0.7645 0.7615

1 1 1 1 1 1 1 1 1

1.0840 1.0900 1.0900 1.1050 1.1250 1.1890 1.2210 1.4170 1.4190 1.42500.0442 0.0432 0.0416 0.0355 0.0765 0.0759 0.0652 0.0492 0.0671 0.07760.6996 0.7167 0.7357 0.6918 0.7030 0.7529 0.7188 0.6459 0.6806 0.67150.0718 0.0612 0.0583 0.0727 0.0598 0.0660 0.0702 0.0586 0.0650 0.06780.0393 0.0326 0.0300 0.0404 0.0326 0.0328 0.0372 0.0349 0.0367 0.03890.0719 0.0564 0.0564 0.0554 0.0564 0.0564 0.0564 0.0564 0.0719 0.05540.5473 0.5782 0.5320 0.7290 0.5784 0.5824 0.6608 0.6191 0.5112 0.7021

1.2290 1.3280 1.3650 1.3710 1.3910 1.4630 1.4720 1.6250 1.6970 1.75900.0379 0.0491 0.0577 0.0635 0.0633 0.0806 0.0603 0.0917 0.1352 0.05440.5655 0.5657 0.6568 0.6481 0.7381 0.6845 0.6439 0.5189 0.6905 0.49270.0893 0.0800 0.0645 0.0775 0.0773 0.0839 0.0812 0.0830 0.0832 0.09770.0589 0.0527 0.0378 0.0460 0.0396 0.0471 0.0485 0.0576 0.0463 0.06960.0696 0.0599 0.0696 0.0599 0.0599 0.0696 0.0599 0.0696 0.0696 0.06960.8454 0.8800 0.5430 0.7684 0.6610 0.6771 0.8097 0.8271 0.6650 0.9992

1 1 1 1 1 1 1 1 1

1.1070 1.1190 1.1200 1.1760 1.1760 1.1780 1.3170 1.3310 1.3980 1.40900.0349 0.0219 0.0100 0.0190 0.0333 0.0320 0.0512 0.0894 0.0998 0.12850.5428 0.5819 0.6524 0.5426 0.7114 0.7325 0.5689 0.3774 0.5859 0.51690.0585 0.0491 0.0632 0.0531 0.0519 0.0586 0.0617 0.0704 0.0656 0.09080.0396 0.0318 0.0373 0.0359 0.0279 0.0303 0.0405 0.0555 0.0422 0.06310.0570 0.0570 0.0391 0.0391 0.0570 0.0570 0.0391 0.0570 0.0570 0.05700.6942 0.5572 0.9527 0.9188 0.4889 0.5315 1.0360 0.9737 0.7405 1.1070

1 1 1 1 1 1 1 1 1

1.0930 1.1030 1.1190 1.1350 1.1650 1.1750 1.2050 1.2120 1.2410 1.32000.0187 0.0154 0.0217 0.0160 0.0139 0.0242 0.0246 0.0333 0.0584 0.15180.5328 0.2693 0.4001 0.4531 0.0756 0.4872 0.2704 0.3962 0.1908 0.36130.0606 0.0651 0.0590 0.0603 0.1061 0.0630 0.0542 0.0705 0.0602 0.07550.0415 0.0556 0.0457 0.0446 0.1020 0.0451 0.0463 0.0548 0.0542 0.06030.0355 0.0463 0.0355 0.0464 0.0464 0.0355 0.0464 0.0463 0.0463 0.04631.1660 1.2010 1.2860 0.9609 2.1980 1.2690 0.9971 1.1840 1.1700 1.3030

1 1 1 1 1 1 1 1 1

1.0320 1.0940 1.1270 1.1280 1.1400 1.1500 1.1880 1.3350 1.3820 1.41800.0590 0.0668 0.0585 0.0539 0.0446 0.0463 0.0537 0.0925 0.0633 0.08360.5637 0.2128 0.4912 0.4206 0.5153 0.5285 0.3798 0.3056 0.3472 0.44960.0621 0.0624 0.0761 0.0663 0.0931 0.0752 0.0843 0.0946 0.0830 0.09700.0410 0.0554 0.0543 0.0505 0.0648 0.0517 0.0664 0.0789 0.0671 0.07200.0376 0.0376 0.0376 0.0740 0.0402 0.0765 0.0402 0.0375 0.0402 0.04021.0910 1.4720 1.4420 0.6819 1.6110 0.6750 1.6500 2.1010 1.6680 1.7890

1 1 1 1 1 1 1 1 1

0.9931 1.0500 1.0870 1.1060 1.1490 1.2170 1.2770 1.3360 1.3710 1.42900.0353 0.0437 0.0532 0.0396 0.0481 0.0580 0.1027 0.1102 0.0388 0.05100.5152 0.4914 0.6708 0.5798 0.6411 0.3481 0.6240 0.5120 0.5132 0.55680.0472 0.0476 0.0527 0.0465 0.0472 0.0504 0.0482 0.0572 0.0482 0.06390.0329 0.0340 0.0303 0.0301 0.0283 0.0407 0.0296 0.0399 0.0336 0.04260.0443 0.0461 0.0452 0.0461 0.0443 0.0443 0.0444 0.0443 0.0443 0.04430.7412 0.7370 0.6702 0.6536 0.6387 0.9191 0.6660 0.9023 0.7590 0.9613









TABLE12d:1Value=Weighted1NYSE1Market1Portfolio111111111+1111111201Single=Sort1Test1Portfolios1Built1Using1Value=Weighted1SecuritiesSAMPLE1STATISTICS1FOR1FOUR1SECLECTED1ESTIMATION1PERIODS1(test1portfolios111=20)1



�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


34

Statistics 1 2 3 4 5 6 7 8 9 10 11 12 131 1 1 1 1 1 1 1 1 1 1 1 11

0.1982 0.2179 0.3416 0.3583 0.5905 0.6921 0.7318 0.7658 0.8538 0.8645 0.9063 0.9174 0.94490.1655 0.1886 0.2127 0.1740 0.0517 0.0345 0.0289 0.0208 0.0150 0.0119 0.0088 0.0099 0.00720.7807 0.7807 0.7807 0.7807 0.7807 0.7807 0.7807 0.7807 0.7807 0.7807 0.7807 0.7807 0.78070.1164 0.0835 0.0637 0.0834 0.1104 0.0890 0.0958 0.1034 0.1084 0.1285 0.0978 0.1113 0.10470.0545 0.0242 0.0196 0.0243 0.0509 0.0169 0.0277 0.0226 0.0289 0.0579 0.0348 0.0332 0.02290.0537 0.0537 0.0537 0.0537 0.0537 0.0537 0.0537 0.0537 0.0537 0.0537 0.0537 0.0598 0.05981.0140 0.4500 0.3650 0.4520 0.9472 0.3138 0.5155 0.4213 0.5374 1.0770 0.6478 0.5552 0.3833

1 1 1 1 1 1 1 1 1 1 1 1

0.2612 0.4558 0.4567 0.6069 0.6995 0.6996 0.7051 0.7606 0.9002 0.9152 0.9486 0.9797 1.14200.0440 0.0040 0.0034 0.0112 0.0384 0.0043 0.0248 0.0179 0.0302 0.0069 0.0177 0.0261 0.04220.6997 0.8142 0.7765 0.7839 0.8552 0.9186 0.8782 0.8538 0.8844 0.8599 0.8863 0.9125 0.94460.03643 0.0411 0.0364 0.0482 0.0533 0.0443 0.0507 0.0459 0.0569 0.0594 0.0554 0.0550 0.06410.01996 0.0177 0.0172 0.0224 0.0203 0.0127 0.0177 0.0175 0.0194 0.0222 0.0187 0.0163 0.01510.0460 0.0460 0.0460 0.0460 0.0460 0.0460 0.0460 0.0460 0.0460 0.0460 0.0483 0.0460 0.04830.4340 0.3849 0.3745 0.4867 0.4409 0.2748 0.3846 0.3811 0.4204 0.4829 0.3870 0.3536 0.3122

1 1 1 1 1 1 1 1 1 1 1 1

0.4506 0.4838 0.5846 0.5904 0.6644 0.6909 0.7289 0.7746 0.8179 0.8277 0.8549 0.9368 0.93830.0384 0.0370 0.0138 0.0336 0.0367 0.0307 0.0330 0.0372 0.0232 0.0304 0.0488 0.0275 0.02950.7100 0.6700 0.7000 0.8189 0.7896 0.8062 0.8623 0.8876 0.8449 0.8678 0.9234 0.9153 0.93900.02253 0.0229 0.0251 0.0235 0.0339 0.0348 0.0356 0.0351 0.0309 0.0388 0.0391 0.0372 0.03960.01213 0.0131 0.0137 0.0100 0.0156 0.0153 0.0132 0.0118 0.0122 0.0141 0.0108 0.0108 0.00980.0331 0.0331 0.0331 0.0331 0.0331 0.0331 0.0331 0.0331 0.0331 0.0331 0.0389 0.0331 0.03890.3670 0.3972 0.4151 0.3024 0.4708 0.4630 0.3999 0.3565 0.3680 0.4269 0.2788 0.3274 0.2521

1 1 1 1 1 1 1 1 1 1 1 1

0.5790 0.5960 0.6217 0.6464 0.7447 0.8657 0.8691 0.8721 0.9045 0.9316 0.9847 1.0230 1.08200.0767 0.0283 0.0321 0.0145 0.0245 0.0121 0.0093 0.0156 0.0072 0.0144 0.0099 0.0168 0.03640.7842 0.8143 0.8425 0.8224 0.8730 0.9125 0.9326 0.9256 0.9235 0.8813 0.9089 0.9202 0.92140.03031 0.0345 0.0370 0.0334 0.0400 0.0348 0.0385 0.0421 0.0388 0.0419 0.0396 0.0440 0.04590.01408 0.0149 0.0147 0.0141 0.0143 0.0103 0.0100 0.0115 0.0107 0.0144 0.0119 0.0124 0.01290.0406 0.0406 0.0406 0.0406 0.0406 0.0406 0.0406 0.0406 0.0435 0.0406 0.0406 0.0406 0.04350.3466 0.3659 0.3616 0.3464 0.3512 0.2537 0.2464 0.2824 0.2466 0.3550 0.2939 0.3064 0.2962

1 1 1 1 1 1 1 1 1 1 1 1

0.5769 0.5919 0.6742 0.6768 0.6784 0.8338 0.8363 0.8601 0.8678 0.8856 0.8879 0.9121 0.98820.0324 0.0153 0.0324 0.0248 0.0149 0.0529 0.0443 0.0420 0.0299 0.0243 0.0127 0.0154 0.01060.6408 0.6920 0.6702 0.8007 0.8441 0.7977 0.8517 0.9170 0.9269 0.9102 0.8841 0.9175 0.92990.03835 0.0409 0.0377 0.0436 0.0553 0.0388 0.0416 0.0470 0.0539 0.0704 0.0461 0.0505 0.05340.02298 0.0227 0.0216 0.0195 0.0218 0.0175 0.0160 0.0136 0.0146 0.0211 0.0157 0.0145 0.01410.0453 0.0453 0.0453 0.0453 0.0453 0.0453 0.0453 0.0453 0.0453 0.0515 0.0453 0.0515 0.04530.5076 0.5010 0.4778 0.4302 0.4820 0.3858 0.3540 0.2992 0.3214 0.4095 0.3466 0.2814 0.3120

0.4459 0.4848 0.6120 0.6449 0.6502 0.6589 0.6869 0.7484 0.8191 0.8378 0.8512 0.8781 0.88420.0503 0.0343 0.0169 0.0121 0.0197 0.0226 0.0249 0.0265 0.0149 0.0110 0.0147 0.0278 0.02120.6986 0.7524 0.8268 0.8196 0.8361 0.8506 0.9079 0.8742 0.9142 0.9472 0.9093 0.9236 0.91160.0524 0.0480 0.0482 0.0466 0.0580 0.0492 0.0523 0.0528 0.0577 0.0543 0.0575 0.0571 0.06010.02877 0.0239 0.0201 0.0198 0.0235 0.0190 0.0159 0.0187 0.0169 0.0125 0.0173 0.0158 0.01790.0490 0.0490 0.0490 0.0490 0.0490 0.0490 0.0490 0.0490 0.0490 0.0490 0.0490 0.0490 0.05180.5868 0.4868 0.4091 0.4032 0.4788 0.3878 0.3234 0.3821 0.3449 0.2544 0.3529 0.3220 0.3453

1 1 1 1 1 1 1 1 1 1 1 1

0.5663 0.5685 0.6048 0.6368 0.6989 0.7365 0.7461 0.7755 0.8123 0.8321 0.8338 0.8868 0.89440.0831 0.0623 0.0253 0.0164 0.0167 0.0147 0.0063 0.0153 0.0045 0.0281 0.0337 0.0306 0.03360.3503 0.3700 0.7861 0.7844 0.7333 0.6313 0.8779 0.8708 0.9046 0.8660 0.8839 0.8995 0.89190.02978 0.0304 0.0341 0.0393 0.0495 0.0359 0.0365 0.0402 0.0470 0.0474 0.0447 0.0456 0.04900.02401 0.0241 0.0158 0.0182 0.0255 0.0218 0.0128 0.0144 0.0145 0.0174 0.0152 0.0145 0.01610.0465 0.0465 0.0465 0.0465 0.0465 0.0465 0.0465 0.0465 0.0465 0.0465 0.0467 0.0465 0.04650.5162 0.5183 0.3396 0.3922 0.5491 0.4690 0.2745 0.3105 0.3117 0.3730 0.3262 0.3112 0.3466

1 1 1 1 1 1 1 1 1 1 1 1

0.3768 0.3826 0.4595 0.6799 0.7064 0.7243 0.8467 0.9220 0.9564 0.9692 1.0120 1.0530 1.06300.0441 0.0239 0.0273 0.0443 0.0196 0.0574 0.0257 0.0138 0.0168 0.0128 0.0277 0.0334 0.01480.2734 0.3217 0.3434 0.5562 0.6450 0.7639 0.7830 0.7747 0.7310 0.7161 0.7984 0.8558 0.82070.02403 0.0269 0.0296 0.0330 0.0351 0.0347 0.0391 0.0403 0.0381 0.0407 0.0437 0.0432 0.04610.02048 0.0221 0.0240 0.0220 0.0209 0.0168 0.0182 0.0191 0.0198 0.0217 0.0196 0.0164 0.01950.0341 0.0341 0.0341 0.0341 0.0341 0.0341 0.0341 0.0341 0.0341 0.0341 0.0436 0.0341 0.03410.6010 0.6487 0.7048 0.6444 0.6144 0.4942 0.5341 0.5612 0.5796 0.6360 0.4500 0.4808 0.5732

1 1 1 1 1 1 1 1 1 1 1 1

0.2724 0.3200 0.3237 0.4746 0.6061 0.7194 0.7586 0.7935 0.7987 0.8390 0.9370 0.9388 0.94690.0433 0.0420 0.0240 0.0428 0.0575 0.0289 0.0276 0.0413 0.0322 0.0365 0.0206 0.0243 0.02420.1808 0.2887 0.1527 0.2102 0.4903 0.7030 0.5486 0.7944 0.7368 0.5715 0.7143 0.8191 0.78820.0212 0.0370 0.0419 0.0416 0.0455 0.0421 0.0433 0.0470 0.0490 0.0551 0.0512 0.0477 0.05400.01919 0.0312 0.0386 0.0370 0.0325 0.0229 0.0291 0.0213 0.0251 0.0361 0.0274 0.0203 0.02490.0299 0.0301 0.0299 0.0299 0.0299 0.0299 0.0299 0.0300 0.0299 0.0300 0.0307 0.0300 0.03070.6409 1.0370 1.2880 1.2340 1.0860 0.7662 0.9726 0.7115 0.8390 1.2040 0.8935 0.6781 0.8108

1 1 1 1 1 1 1 1 1 1 1 1

0.0828 0.1077 0.2610 0.4231 0.4888 0.5512 0.6108 0.7213 0.7237 0.7857 0.8590 0.9238 0.92610.0663 0.0598 0.0528 0.0240 0.0531 0.0791 0.0687 0.0348 0.0714 0.0405 0.0183 0.0085 0.00770.0419 0.2880 0.4842 0.4720 0.8177 0.6577 0.7578 0.8084 0.8059 0.6534 0.7833 0.8820 0.81030.02255 0.0272 0.0313 0.0350 0.0331 0.0295 0.0302 0.0355 0.0355 0.0425 0.0328 0.0387 0.03640.02208 0.0229 0.0225 0.0254 0.0141 0.0173 0.0149 0.0155 0.0157 0.0250 0.0153 0.0133 0.01590.0282 0.0282 0.0282 0.0281 0.0282 0.0280 0.0282 0.0281 0.0280 0.0280 0.0281 0.0315 0.02800.7823 0.8132 0.7974 0.9052 0.5004 0.6171 0.5272 0.5527 0.5598 0.8938 0.5433 0.4212 0.5674







TABLE12e:1Equal=Weighted1NYSE1Market1Portfolio111111111+11111115x51Double=Sort1Test1Portfolios1Built1Using1Equal=Weighted1SecuritiesSAMPLE1STATISTICS1FOR1FOUR1SECLECTED1ESTIMATION1PERIODS1(test1portfolios11=13)





�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


35

1 1 1 1 1 1 1 1 1 1 1 1Statistics 14 15 16 17 18 19 20 21 22 23 24 25

1 1 1 1 1 1 1 1 1 1 1 1

0.9547 1.0390 1.1280 1.1440 1.1450 1.2580 1.2950 1.3200 1.3360 1.3570 1.3810 1.44600.0126 0.0203 0.0348 0.0436 0.0471 0.0291 0.0307 0.0337 0.0319 0.0621 0.0670 0.02790.7807 0.7807 0.7807 0.7807 0.7807 0.7807 0.7807 0.7807 0.7807 0.7807 0.7807 0.78070.1174 0.1332 0.0870 0.1033 0.1396 0.1458 0.1244 0.1155 0.1232 0.1385 0.1368 0.13000.0372 0.0524 0.0286 0.0269 0.0512 0.0480 0.0506 0.0321 0.0329 0.0403 0.0396 0.04690.0537 0.0598 0.0598 0.0598 0.0598 0.0598 0.0598 0.0598 0.0598 0.0598 0.0615 0.05980.6930 0.8762 0.4787 0.4505 0.8563 0.8025 0.8457 0.5373 0.5496 0.6745 0.6434 0.7839

1 1 1 1 1 1 1 1 1 1 1 1

1.1690 1.1700 1.1710 1.2380 1.2500 1.2580 1.3070 1.3130 1.3470 1.4420 1.4570 1.53600.0414 0.0090 0.0156 0.0139 0.0046 0.0021 0.0172 0.0449 0.0374 0.0285 0.0365 0.03020.9067 0.8655 0.9008 0.9297 0.9178 0.8738 0.8251 0.9191 0.8072 0.8357 0.8654 0.94430.0677 0.0834 0.0764 0.0683 0.0728 0.0894 0.0913 0.0774 0.1124 0.1097 0.1099 0.08600.0207 0.0306 0.0241 0.0181 0.0209 0.0317 0.0382 0.0220 0.0493 0.0445 0.0403 0.02030.0460 0.0483 0.0483 0.0483 0.0483 0.0483 0.0483 0.0483 0.0483 0.0483 0.0548 0.04830.4491 0.6332 0.4984 0.3751 0.4323 0.6571 0.7906 0.4555 1.0220 0.9204 0.7365 0.4201

1 1 1 1 1 1 1 1 1 1 1 1

0.9428 1.0200 1.0510 1.0640 1.0700 1.0920 1.2640 1.3590 1.5440 1.5880 1.6180 1.62700.0305 0.0013 0.0243 0.0288 0.0328 0.0379 0.0190 0.0185 0.0742 0.0750 0.0819 0.07170.8832 0.8985 0.9538 0.9281 0.9185 0.9117 0.8472 0.9135 0.9170 0.9079 0.8377 0.72250.0365 0.0407 0.0458 0.0441 0.0462 0.0453 0.0439 0.0565 0.0547 0.0568 0.0546 0.05330.0125 0.0130 0.0098 0.0118 0.0132 0.0135 0.0172 0.0166 0.0158 0.0172 0.0220 0.02810.0331 0.0389 0.0389 0.0389 0.0389 0.0389 0.0389 0.0389 0.0433 0.0389 0.0389 0.03890.3778 0.3336 0.2534 0.3046 0.3393 0.3469 0.4418 0.4274 0.3637 0.4434 0.5659 0.7225

1 1 1 1 1 1 1 1 1 1 1 1

1.0990 1.1260 1.1590 1.1740 1.1910 1.1940 1.1950 1.3250 1.3310 1.3320 1.3360 1.36200.0318 0.0232 0.0325 0.0233 0.0161 0.0125 0.0274 0.0129 0.0245 0.0255 0.0285 0.12220.9174 0.8455 0.9003 0.9024 0.8930 0.9253 0.8874 0.8998 0.8947 0.9273 0.9129 0.80210.0447 0.0501 0.0465 0.0442 0.0465 0.0555 0.0526 0.0522 0.0579 0.0545 0.0528 0.06010.0129 0.0197 0.0147 0.0138 0.0152 0.0152 0.0177 0.0165 0.0188 0.0147 0.0156 0.02670.0435 0.0434 0.0435 0.0435 0.0435 0.0435 0.0406 0.0435 0.0435 0.0435 0.0434 0.05110.2957 0.4533 0.3379 0.3174 0.3499 0.3488 0.4344 0.3799 0.4320 0.3379 0.3588 0.5225

1 1 1 1 1 1 1 1 1 1 1 1

0.9958 1.0040 1.1150 1.1350 1.1480 1.1500 1.1730 1.1780 1.1950 1.2620 1.3200 1.37200.0111 0.0114 0.0384 0.0236 0.0109 0.0163 0.0261 0.0380 0.0344 0.0482 0.0519 0.05670.9390 0.9251 0.9185 0.9378 0.9389 0.9151 0.8907 0.8945 0.9202 0.9308 0.9212 0.91410.0562 0.0653 0.0494 0.0591 0.0552 0.0679 0.0728 0.0611 0.0623 0.0645 0.0661 0.08530.0139 0.0179 0.0141 0.0147 0.0137 0.0198 0.0241 0.0199 0.0176 0.0170 0.0186 0.02500.0515 0.0515 0.0515 0.0515 0.0453 0.0515 0.0515 0.0515 0.0515 0.0515 0.0515 0.05960.2695 0.3465 0.2737 0.2861 0.3014 0.3841 0.4669 0.3853 0.3419 0.3292 0.3601 0.4196

0.9132 0.9216 1.0090 1.0380 1.0550 1.1270 1.1550 1.1720 1.2630 1.3490 1.3560 1.40100.0151 0.0218 0.0141 0.0215 0.0154 0.0290 0.0283 0.0264 0.0218 0.0451 0.0248 0.03310.9194 0.9133 0.9175 0.9225 0.9500 0.9596 0.8927 0.9319 0.9433 0.9206 0.9205 0.86740.0691 0.0720 0.0644 0.0688 0.0684 0.0759 0.0795 0.0776 0.0826 0.0825 0.0981 0.09030.0196 0.0212 0.0185 0.0192 0.0153 0.0153 0.0260 0.0203 0.0197 0.0232 0.0277 0.03290.0518 0.0518 0.0518 0.0518 0.0518 0.0518 0.0518 0.0518 0.0518 0.0518 0.0518 0.05800.3790 0.4097 0.3575 0.3699 0.2956 0.2947 0.5029 0.3913 0.3798 0.4488 0.5345 0.5670

1 1 1 1 1 1 1 1 1 1 1 1

0.9534 0.9700 0.9831 1.0010 1.0560 1.0630 1.1800 1.1830 1.2470 1.2510 1.3130 1.47700.0215 0.0199 0.0232 0.0245 0.0153 0.0425 0.0077 0.0135 0.0064 0.0303 0.0284 0.05630.9158 0.9024 0.9144 0.9238 0.9172 0.8773 0.8885 0.8873 0.9168 0.7976 0.8603 0.85760.0479 0.0484 0.0491 0.0456 0.0466 0.0491 0.0516 0.0491 0.0548 0.0532 0.0562 0.07350.0139 0.0151 0.0144 0.0126 0.0134 0.0172 0.0172 0.0165 0.0158 0.0239 0.0210 0.02770.0467 0.0467 0.0467 0.0467 0.0467 0.0467 0.0467 0.0467 0.0467 0.0467 0.0467 0.05430.2976 0.3244 0.3077 0.2696 0.2873 0.3688 0.3691 0.3531 0.3388 0.5131 0.4506 0.5106

1 1 1 1 1 1 1 1 1 1 1 1

1.0730 1.0800 1.0810 1.0980 1.1000 1.1040 1.1340 1.1710 1.1890 1.2810 1.2890 1.30700.0202 0.0201 0.0188 0.0102 0.0099 0.0130 0.0076 0.0169 0.0135 0.0278 0.0248 0.03600.8080 0.8183 0.8234 0.8309 0.7904 0.8261 0.6210 0.8839 0.8346 0.7953 0.3198 0.69490.0473 0.0509 0.0500 0.0489 0.0438 0.0521 0.0631 0.0576 0.0581 0.0654 0.0690 0.06910.0207 0.0217 0.0210 0.0201 0.0201 0.0218 0.0389 0.0196 0.0236 0.0296 0.0569 0.03810.0436 0.0436 0.0436 0.0436 0.0436 0.0436 0.0438 0.0438 0.0438 0.0438 0.0438 0.04350.4753 0.4976 0.4811 0.4603 0.4594 0.4983 0.8875 0.4481 0.5399 0.6752 1.3000 0.8767

1 1 1 1 1 1 1 1 1 1 1 1

0.9583 0.9779 1.0060 1.0280 1.1340 1.1710 1.2190 1.2580 1.3030 1.3210 1.4670 1.53800.0308 0.0324 0.0506 0.0482 0.0380 0.0361 0.0300 0.0323 0.0283 0.0208 0.0536 0.05290.8517 0.8205 0.7949 0.8326 0.8120 0.8547 0.7467 0.8685 0.8354 0.8698 0.8049 0.74490.0492 0.0557 0.0642 0.0656 0.0699 0.0627 0.0715 0.0707 0.0666 0.0767 0.0787 0.08680.0190 0.0236 0.0291 0.0269 0.0303 0.0239 0.0360 0.0257 0.0270 0.0277 0.0348 0.04380.0307 0.0300 0.0311 0.0311 0.0311 0.0311 0.0311 0.0311 0.0307 0.0311 0.0311 0.05050.6184 0.7881 0.9354 0.8642 0.9748 0.7693 1.1580 0.8256 0.8816 0.8911 1.1190 0.8680

1 1 1 1 1 1 1 1 1 1 1 1

0.9979 1.0300 1.1240 1.1390 1.1470 1.2340 1.2400 1.2700 1.2780 1.2930 1.3220 1.63100.0193 0.0207 0.0103 0.0062 0.0044 0.0190 0.0193 0.0232 0.0216 0.0240 0.0254 0.11590.8766 0.8306 0.7733 0.8334 0.8747 0.8831 0.8094 0.8624 0.8533 0.8384 0.8522 0.78390.0423 0.0499 0.0386 0.0503 0.0496 0.0476 0.0512 0.0511 0.0467 0.0506 0.0508 0.06690.0149 0.0205 0.0184 0.0205 0.0176 0.0163 0.0224 0.0190 0.0179 0.0203 0.0195 0.03110.0317 0.0315 0.0315 0.0317 0.0317 0.0317 0.0318 0.0318 0.0318 0.0318 0.0318 0.04370.4688 0.6514 0.5828 0.6473 0.5537 0.5127 0.7028 0.5956 0.5613 0.6390 0.6135 0.7125









TABLE12e:1Equal=Weighted1NYSE1Market1Portfolio111111111+11111115x51Double=Sort1Test1Portfolios1Built1Using1Equal=Weighted1SecuritiesSAMPLE1STATISTICS1FOR1FOUR1SECLECTED1ESTIMATION1PERIODS1(test1portfolios114=25)1111



�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


36

Statistics 1 2 3 4 5 6 7 8 9 10 11 12 131 1 1 1 1 1 1 1 1 1 1 1 11

0.1982 0.2179 0.3416 0.3583 0.5905 0.6921 0.7318 0.7658 0.8538 0.8645 0.9063 0.9174 0.94490.1374 0.1690 0.1809 0.1454 0.0473 0.0437 0.0456 0.0501 0.0416 0.0459 0.0476 0.0103 0.00720.4741 0.4741 0.4741 0.4741 0.4741 0.4741 0.4741 0.4741 0.4741 0.4741 0.4741 0.4741 0.47410.1519 0.0857 0.0708 0.1063 0.1113 0.0994 0.0896 0.1232 0.1131 0.1273 0.1043 0.1198 0.12170.1102 0.0429 0.0390 0.0562 0.0748 0.0507 0.0446 0.0535 0.0643 0.0686 0.0554 0.0586 0.06680.0487 0.0487 0.0487 0.0487 0.0487 0.0487 0.0487 0.0487 0.0604 0.0487 0.0604 0.0487 0.04872.2640 0.8812 0.8015 1.1540 1.5360 1.0410 0.9158 1.1000 1.0640 1.4090 0.9158 1.2050 1.3730

1 1 1 1 1 1 1 1 1 1 1 1

0.3084 0.4479 0.4954 0.6335 0.6474 0.6586 0.7597 0.8310 0.9167 0.9431 0.9929 1.0300 1.03100.0700 0.0425 0.0475 0.0518 0.0263 0.0409 0.0555 0.0613 0.0511 0.0449 0.0625 0.0695 0.07250.5500 0.3767 0.3692 0.3066 0.6410 0.7781 0.7405 0.5739 0.7157 0.6293 0.8318 0.4657 0.66870.04385 0.0783 0.0482 0.1254 0.0664 0.0579 0.0588 0.0496 0.0596 0.0713 0.0567 0.0780 0.06900.02941 0.0619 0.0383 0.1044 0.0398 0.0273 0.0300 0.0324 0.0318 0.0434 0.0233 0.0570 0.03970.0446 0.0446 0.0446 0.0446 0.0446 0.0446 0.0446 0.0446 0.0446 0.0446 0.0559 0.0559 0.05590.6589 1.3860 0.8582 2.3390 0.8911 0.6111 0.6716 0.7259 0.7122 0.9730 0.4160 1.0200 0.7100

1 1 1 1 1 1 1 1 1 1 1 1

0.3289 0.3910 0.5092 0.6315 0.6773 0.7063 0.7634 0.7835 0.7898 0.8305 0.8733 0.8821 0.94980.0841 0.0881 0.0592 0.0220 0.0280 0.0374 0.0261 0.0296 0.0459 0.0450 0.0337 0.0397 0.02410.3800 0.2926 0.4585 0.4819 0.5108 0.6088 0.6329 0.6523 0.4673 0.5205 0.6944 0.7020 0.63810.02956 0.0296 0.0360 0.0294 0.0430 0.0405 0.0421 0.0444 0.0362 0.0395 0.0447 0.0454 0.05060.02328 0.0249 0.0265 0.0212 0.0301 0.0254 0.0255 0.0262 0.0264 0.0274 0.0247 0.0248 0.03050.0454 0.0454 0.0454 0.0454 0.0454 0.0454 0.0454 0.0454 0.0409 0.0454 0.0454 0.0454 0.04090.5124 0.5474 0.5828 0.4665 0.6616 0.5581 0.5611 0.5760 0.6453 0.6027 0.5436 0.5450 0.7451

1 1 1 1 1 1 1 1 1 1 1 1

0.3473 0.5078 0.6460 0.6498 0.6888 0.7229 0.9016 0.9147 0.9469 0.9627 0.9906 1.0240 1.04400.0744 0.0784 0.0803 0.0457 0.0521 0.0376 0.0484 0.0449 0.0341 0.0355 0.0185 0.0218 0.01940.6004 0.6712 0.5733 0.5605 0.6745 0.7109 0.7289 0.6992 0.6553 0.6163 0.7062 0.5894 0.56690.03479 0.0388 0.0404 0.0420 0.0494 0.0397 0.0484 0.0461 0.0488 0.0509 0.0466 0.0491 0.06410.02199 0.0223 0.0264 0.0278 0.0282 0.0214 0.0252 0.0253 0.0287 0.0316 0.0253 0.0314 0.04220.0402 0.0402 0.0402 0.0402 0.0402 0.0402 0.0402 0.0402 0.0442 0.0442 0.0402 0.0442 0.04020.5476 0.5541 0.6573 0.6930 0.7015 0.5319 0.6278 0.6292 0.6487 0.7142 0.6291 0.7116 1.0510

1 1 1 1 1 1 1 1 1 1 1 1

0.4853 0.5941 0.6209 0.6800 0.7138 0.7627 0.7858 0.7865 0.9102 0.9275 0.9290 0.9562 0.96420.0693 0.0342 0.0320 0.0303 0.0262 0.0351 0.0330 0.0201 0.0513 0.0543 0.0398 0.0368 0.02450.5585 0.5145 0.4710 0.7113 0.6419 0.5885 0.6577 0.6263 0.7245 0.6969 0.6892 0.7027 0.65010.04131 0.0457 0.0443 0.0511 0.0684 0.0432 0.0557 0.0537 0.0645 0.0780 0.0531 0.0644 0.06060.02745 0.0318 0.0322 0.0275 0.0410 0.0277 0.0326 0.0328 0.0339 0.0429 0.0296 0.0351 0.03580.0537 0.0537 0.0537 0.0537 0.0537 0.0537 0.0607 0.0537 0.0537 0.0537 0.0537 0.0607 0.06070.5109 0.5921 0.6000 0.5108 0.7622 0.5161 0.5367 0.6104 0.6305 0.7986 0.5505 0.5784 0.5898

0.3812 0.4045 0.4218 0.5669 0.6105 0.6900 0.7045 0.7284 0.7759 0.8313 0.8332 0.8848 0.91010.0560 0.0640 0.0720 0.0420 0.0390 0.0203 0.0477 0.0633 0.0835 0.0813 0.0827 0.0616 0.05980.6495 0.6109 0.6176 0.6372 0.4542 0.7614 0.6953 0.5537 0.7790 0.7233 0.7401 0.6174 0.57420.05952 0.0533 0.0522 0.0509 0.0687 0.0511 0.0601 0.0496 0.0757 0.0713 0.0558 0.0883 0.05940.03524 0.0333 0.0323 0.0307 0.0507 0.0250 0.0332 0.0331 0.0356 0.0375 0.0284 0.0546 0.03880.0492 0.0492 0.0492 0.0492 0.0492 0.0492 0.0492 0.0535 0.0492 0.0492 0.0492 0.0535 0.04920.7167 0.6763 0.6566 0.6241 1.0320 0.5076 0.6749 0.6195 0.7235 0.7628 0.5782 1.0210 0.7883

1 1 1 1 1 1 1 1 1 1 1 1

0.5588 0.5817 0.5931 0.6048 0.6853 0.7189 0.7325 0.7326 0.7430 0.8472 0.8697 0.8771 0.90940.0814 0.0801 0.0453 0.0469 0.0348 0.0249 0.0163 0.0314 0.0541 0.0432 0.0306 0.0280 0.03220.2291 0.2879 0.5126 0.5573 0.4842 0.4753 0.5658 0.6294 0.6018 0.6754 0.7487 0.6505 0.52740.0318 0.0325 0.0443 0.0462 0.0605 0.0408 0.0466 0.0511 0.0570 0.0533 0.0528 0.0533 0.06050.02793 0.0274 0.0309 0.0308 0.0435 0.0296 0.0307 0.0311 0.0360 0.0304 0.0265 0.0315 0.04160.0456 0.0456 0.0456 0.0456 0.0456 0.0456 0.0456 0.0456 0.0456 0.0456 0.0409 0.0409 0.04560.6120 0.6012 0.6777 0.6741 0.9523 0.6483 0.6726 0.6820 0.7889 0.6654 0.6472 0.7699 0.9108

1 1 1 1 1 1 1 1 1 1 1 1

0.3462 0.3947 0.4087 0.5533 0.6697 0.7832 0.8210 0.8251 0.9501 0.9591 0.9706 1.0170 1.02700.0592 0.0525 0.0507 0.0603 0.0461 0.0465 0.0646 0.0366 0.0516 0.0452 0.0270 0.0303 0.03580.2722 0.2517 0.2295 0.5224 0.4601 0.4360 0.6436 0.5893 0.3385 0.4518 0.5783 0.6128 0.59500.02669 0.0307 0.0304 0.0324 0.0382 0.0413 0.0465 0.0543 0.0484 0.0564 0.0534 0.0686 0.04860.02277 0.0266 0.0267 0.0224 0.0281 0.0310 0.0278 0.0348 0.0394 0.0417 0.0347 0.0427 0.03090.0326 0.0326 0.0326 0.0326 0.0326 0.0423 0.0326 0.0326 0.0326 0.0326 0.0326 0.0326 0.03260.6982 0.8142 0.8180 0.6869 0.8614 0.7330 0.8516 1.0670 1.2070 1.2800 1.0640 1.3090 0.9478

1 1 1 1 1 1 1 1 1 1 1 1

0.1992 0.2303 0.3039 0.3070 0.3135 0.6854 0.7208 0.7504 0.7550 0.8862 0.8888 0.9281 0.93060.0401 0.0521 0.0491 0.0640 0.1516 0.0602 0.0753 0.0833 0.0762 0.0521 0.0400 0.0256 0.03470.1500 0.2428 0.1662 0.1102 0.3860 0.5079 0.2293 0.4512 0.3801 0.2516 0.5662 0.6066 0.61820.02178 0.0402 0.0497 0.0473 0.0788 0.0641 0.0569 0.0581 0.0787 0.0821 0.0537 0.0661 0.06950.02008 0.0350 0.0454 0.0446 0.0617 0.0449 0.0500 0.0431 0.0620 0.0710 0.0354 0.0415 0.04300.0255 0.0255 0.0255 0.0255 0.0255 0.0255 0.0255 0.0254 0.0255 0.0254 0.0254 0.0236 0.02360.7885 1.3700 1.7830 1.7530 2.4250 1.7650 1.9630 1.6930 2.4330 2.7930 1.3910 1.7580 1.8210

1 1 1 1 1 1 1 1 1 1 1 1

0.0828 0.1077 0.2610 0.4231 0.4888 0.5512 0.6108 0.7213 0.7237 0.7857 0.8590 0.9238 0.92610.0512 0.0437 0.0392 0.0208 0.0106 0.0186 0.0327 0.0185 0.0195 0.0090 0.0453 0.0180 0.02030.0274 0.1574 0.3596 0.4008 0.6299 0.4834 0.5618 0.4167 0.4317 0.3190 0.7289 0.6799 0.58510.02457 0.0261 0.0352 0.0412 0.0454 0.0381 0.0356 0.0443 0.0610 0.0544 0.0346 0.0460 0.04690.02423 0.0240 0.0282 0.0319 0.0276 0.0274 0.0236 0.0339 0.0460 0.0449 0.0180 0.0260 0.03020.0252 0.0252 0.0252 0.0252 0.0251 0.0252 0.0252 0.0304 0.0252 0.0251 0.0251 0.0252 0.03040.9599 0.9504 1.1160 1.2640 1.1010 1.0850 0.9365 1.1120 1.8250 1.7880 0.7179 1.0340 0.9913







TABLE12f:1Equal=Weighted1NYSE1Market1Portfolio111111111+11111115x51Double=Sort1Test1Portfolios1Built1Using1Value=Weighted1SecuritiesSAMPLE1STATISTICS1FOR1FOUR1SECLECTED1ESTIMATION1PERIODS1(test1portfolios11=13)





�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


37

1 1 1 1 1 1 1 1 1 1 1 1Statistics 14 15 16 17 18 19 20 21 22 23 24 25

1 1 1 1 1 1 1 1 1 1 1 1

0.9547 1.0390 1.1280 1.1440 1.1450 1.2580 1.2950 1.3200 1.3360 1.3570 1.3810 1.44600.0355 0.0237 0.0367 0.0409 0.0466 0.0303 0.0265 0.0430 0.0533 0.0726 0.1293 0.46070.4741 0.4741 0.4741 0.4741 0.4741 0.4741 0.4741 0.4741 0.4741 0.4741 0.4741 0.47410.1397 0.1681 0.0809 0.1150 0.1580 0.1470 0.1520 0.1340 0.1319 0.1514 0.1371 0.12630.0857 0.1098 0.0424 0.0673 0.0689 0.0748 0.1074 0.0674 0.0743 0.0875 0.0632 0.05930.0604 0.0604 0.0604 0.0604 0.0487 0.0604 0.0604 0.0604 0.0604 0.0604 0.0604 0.06041.4170 1.8180 0.7014 1.1130 1.4150 1.2380 1.7780 1.1150 1.2300 1.4490 1.0460 0.9814

1 1 1 1 1 1 1 1 1 1 1 1

1.0780 1.0990 1.2190 1.2420 1.2950 1.3380 1.3830 1.4210 1.4920 1.5190 1.5300 1.56600.0434 0.0403 0.0391 0.0341 0.0407 0.0566 0.0648 0.0864 0.1226 0.0700 0.1041 0.15380.5820 0.5683 0.7085 0.6561 0.5793 0.6759 0.6306 0.7507 0.5858 0.5792 0.6255 0.77430.0755 0.0902 0.0847 0.0955 0.0956 0.1050 0.0872 0.0744 0.1310 0.1293 0.0964 0.09860.0488 0.0593 0.0457 0.0560 0.0620 0.0598 0.0530 0.0371 0.0843 0.0839 0.0590 0.04690.0446 0.0446 0.0559 0.0559 0.0559 0.0559 0.0559 0.0559 0.0559 0.0559 0.0584 0.05591.0940 1.3280 0.8177 1.0020 1.1090 1.0690 0.9476 0.6644 1.5080 1.5000 1.0090 0.8381

1 1 1 1 1 1 1 1 1 1 1 1

1.0450 1.1070 1.1310 1.1340 1.1860 1.3940 1.4700 1.4750 1.5310 1.5620 1.7490 2.17300.0405 0.0324 0.0373 0.0409 0.0311 0.0784 0.1001 0.0814 0.0919 0.0776 0.1325 0.25180.4492 0.7404 0.7790 0.6893 0.6548 0.5581 0.5088 0.6959 0.8154 0.5272 0.4860 0.40730.0398 0.0540 0.0567 0.0485 0.0492 0.0506 0.0583 0.0586 0.0631 0.0703 0.0694 0.08570.0296 0.0275 0.0267 0.0270 0.0289 0.0336 0.0409 0.0323 0.0271 0.0484 0.0498 0.06600.0418 0.0409 0.0409 0.0409 0.0409 0.0409 0.0454 0.0409 0.0409 0.0409 0.0409 0.04090.7073 0.6726 0.6518 0.6612 0.7064 0.8222 0.8994 0.7906 0.6628 1.1820 1.2170 1.6140

1 1 1 1 1 1 1 1 1 1 1 1

1.0760 1.1490 1.1760 1.1840 1.2060 1.2230 1.2470 1.3480 1.3550 1.3670 1.4670 1.88000.0254 0.0429 0.0503 0.0521 0.0528 0.0182 0.0190 0.0316 0.0231 0.0346 0.1239 0.12620.7820 0.6404 0.7774 0.6868 0.5764 0.7393 0.7252 0.7051 0.6957 0.5673 0.7171 0.49750.0514 0.0719 0.0547 0.0662 0.0581 0.0663 0.0661 0.0533 0.0655 0.0652 0.0660 0.06810.0240 0.0431 0.0258 0.0370 0.0378 0.0339 0.0347 0.0290 0.0361 0.0429 0.0351 0.04830.0442 0.0442 0.0442 0.0442 0.0402 0.0442 0.0442 0.0402 0.0442 0.0442 0.0442 0.05740.5428 0.9759 0.5845 0.8385 0.9407 0.7667 0.7848 0.7207 0.8173 0.9709 0.7945 0.8417

1 1 1 1 1 1 1 1 1 1 1 1

0.9680 1.0190 1.0560 1.0640 1.0780 1.1580 1.1900 1.2490 1.2550 1.3090 1.3520 1.39800.0126 0.0303 0.0355 0.0439 0.0477 0.0274 0.0411 0.0864 0.0715 0.0611 0.0970 0.13410.6855 0.6861 0.7573 0.7774 0.6913 0.7151 0.7143 0.7251 0.7411 0.6526 0.7498 0.75250.0617 0.0874 0.0601 0.0659 0.0583 0.0778 0.0846 0.0736 0.0649 0.0703 0.0706 0.08610.0346 0.0490 0.0296 0.0311 0.0324 0.0415 0.0452 0.0386 0.0330 0.0415 0.0353 0.04280.0537 0.0607 0.0537 0.0607 0.0607 0.0607 0.0607 0.0607 0.0607 0.0607 0.0498 0.06070.6438 0.8062 0.5513 0.5119 0.5329 0.6837 0.7446 0.6350 0.5436 0.6826 0.7098 0.7050

0.9360 0.9674 0.9684 1.0200 1.0310 1.0550 1.1560 1.1820 1.3030 1.3280 1.3370 1.58400.0711 0.0597 0.0648 0.0640 0.0448 0.0293 0.0541 0.0784 0.0792 0.0653 0.0911 0.06760.6958 0.7152 0.8217 0.8266 0.6652 0.7718 0.7471 0.7677 0.8067 0.7223 0.6925 0.75240.0869 0.0814 0.0760 0.0918 0.0702 0.0787 0.1389 0.0848 0.0864 0.0903 0.0960 0.09160.0480 0.0434 0.0321 0.0382 0.0406 0.0376 0.0699 0.0409 0.0380 0.0476 0.0532 0.04560.0535 0.0535 0.0535 0.0492 0.0535 0.0535 0.0535 0.0535 0.0535 0.0535 0.0535 0.05410.8969 0.8125 0.6003 0.7776 0.7596 0.7034 1.3070 0.7643 0.7101 0.8903 0.9953 0.8417

1 1 1 1 1 1 1 1 1 1 1 1

0.9155 0.9318 0.9506 0.9649 0.9993 1.1440 1.1670 1.1690 1.2180 1.2550 1.3490 1.45100.0320 0.0382 0.0373 0.0400 0.0484 0.0388 0.0333 0.0621 0.0734 0.0708 0.0719 0.07720.6051 0.5569 0.5782 0.6823 0.7851 0.6610 0.5956 0.7083 0.7309 0.4103 0.6267 0.47570.0495 0.0637 0.0627 0.0520 0.0582 0.0543 0.0542 0.0642 0.0702 0.0744 0.0632 0.10040.0311 0.0424 0.0407 0.0293 0.0270 0.0316 0.0344 0.0347 0.0364 0.0571 0.0386 0.07270.0409 0.0409 0.0409 0.0409 0.0456 0.0409 0.0409 0.0409 0.0409 0.0409 0.0409 0.05590.7608 1.0370 0.9957 0.7163 0.5916 0.7732 0.8423 0.8478 0.8908 1.3970 0.9443 1.3010

1 1 1 1 1 1 1 1 1 1 1 1

1.0330 1.0360 1.0490 1.0660 1.0730 1.0890 1.1000 1.1120 1.2380 1.2660 1.2680 1.33100.0362 0.0094 0.0245 0.0307 0.0273 0.0277 0.0326 0.0381 0.0158 0.0178 0.0799 0.12130.3820 0.4980 0.5356 0.4681 0.2847 0.4575 0.1059 0.5410 0.2727 0.4037 0.2231 0.42770.0603 0.0734 0.0603 0.0742 0.0528 0.0675 0.0796 0.0678 0.1352 0.0917 0.0783 0.08070.0474 0.0520 0.0411 0.0541 0.0447 0.0497 0.0753 0.0459 0.1153 0.0708 0.0690 0.06100.0423 0.0423 0.0423 0.0423 0.0423 0.0423 0.0423 0.0423 0.0423 0.0423 0.0450 0.04231.1210 1.2300 0.9729 1.2810 1.0570 1.1770 1.7800 1.0860 2.7270 1.6740 1.5330 1.4430

1 1 1 1 1 1 1 1 1 1 1 1

0.9658 0.9659 1.0370 1.1310 1.1510 1.1560 1.2260 1.2470 1.2890 1.4950 1.5200 1.75200.0285 0.0339 0.0414 0.0311 0.0393 0.0631 0.0552 0.0527 0.0742 0.0943 0.0490 0.21880.4774 0.3912 0.5852 0.6431 0.4807 0.5078 0.4573 0.6318 0.6583 0.6218 0.4864 0.50430.0592 0.0829 0.0724 0.0747 0.0840 0.1011 0.1159 0.0819 0.0834 0.0895 0.0953 0.12690.0428 0.0646 0.0466 0.0446 0.0605 0.0709 0.0854 0.0497 0.0487 0.0550 0.0683 0.08940.0240 0.0236 0.0254 0.0240 0.0240 0.0240 0.0236 0.0240 0.0240 0.0240 0.0432 0.02401.7850 2.7390 1.8340 1.8620 2.5270 2.9610 3.6180 2.0750 2.0350 2.2980 1.5800 3.7300

1 1 1 1 1 1 1 1 1 1 1 1

0.9979 1.0300 1.1240 1.1390 1.1470 1.2340 1.2400 1.2700 1.2780 1.2930 1.3220 1.63100.0218 0.0196 0.0179 0.0195 0.0287 0.0137 0.0294 0.0290 0.0448 0.0443 0.0531 0.09630.4092 0.6291 0.7061 0.6650 0.5819 0.6250 0.4964 0.5935 0.7056 0.6266 0.6071 0.50630.0472 0.0562 0.0489 0.0573 0.0593 0.0498 0.0636 0.0538 0.0531 0.0628 0.0639 0.06950.0363 0.0342 0.0265 0.0332 0.0384 0.0305 0.0452 0.0343 0.0288 0.0384 0.0401 0.04880.0304 0.0251 0.0305 0.0305 0.0305 0.0305 0.0305 0.0305 0.0305 0.0305 0.0305 0.04311.1920 1.3640 0.8704 1.0890 1.2600 1.0010 1.4820 1.1260 0.9459 1.2600 1.3160 1.1330









TABLE12f:1Equal=Weighted1NYSE1Market1Portfolio111111111+11111115x51Double=Sort1Test1Portfolios1Built1Using1Value=Weighted1SecuritiesSAMPLE1STATISTICS1FOR1FOUR1SECLECTED1ESTIMATION1PERIODS1(test1portfolios114=25)111



�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


38

Statistics 1 2 3 4 5 6 7 8 9 10 11 12 131 1 1 1 1 1 1 1 1 1 1 1 11

0.1982 0.2179 0.3416 0.3583 0.5905 0.6921 0.7318 0.7658 0.8538 0.8645 0.9063 0.9174 0.94490.2895 0.2822 0.3083 0.3186 0.2218 0.2056 0.2037 0.1869 0.1853 0.1765 0.1725 0.1716 0.18310.7242 0.7242 0.7242 0.7242 0.7242 0.7242 0.7242 0.7242 0.7242 0.7242 0.7242 0.7242 0.72420.1076 0.0781 0.0708 0.0867 0.1351 0.1020 0.0998 0.0913 0.1011 0.1398 0.0958 0.0999 0.12000.0565 0.0219 0.0224 0.0324 0.0803 0.0335 0.0347 0.0224 0.0403 0.0928 0.0242 0.0250 0.04430.0488 0.0488 0.0488 0.0488 0.0488 0.0488 0.0488 0.0488 0.0488 0.0488 0.0488 0.0592 0.05921.1590 0.4490 0.4602 0.6638 1.6460 0.6865 0.7123 0.4592 0.8273 1.9030 0.4952 0.4217 0.7493

1 1 1 1 1 1 1 1 1 1 1 1

0.4600 0.6638 0.7427 0.9694 1.0190 1.0500 1.0990 1.2700 1.3290 1.3760 1.4120 1.5520 1.59000.0692 0.0229 0.0094 0.0935 0.0273 0.0367 0.0265 0.0406 0.0423 0.0439 0.0480 0.0616 0.02790.6997 0.8142 0.7765 0.7839 0.8552 0.9186 0.8782 0.8538 0.8844 0.8599 0.8863 0.9125 0.94460.03643 0.0411 0.0364 0.0482 0.0533 0.0443 0.0507 0.0459 0.0569 0.0594 0.0554 0.0550 0.06410.01996 0.0177 0.0172 0.0224 0.0203 0.0127 0.0177 0.0175 0.0194 0.0222 0.0187 0.0163 0.01510.0460 0.0460 0.0460 0.0460 0.0460 0.0460 0.0460 0.0460 0.0460 0.0460 0.0483 0.0460 0.04830.4340 0.3849 0.3745 0.4867 0.4409 0.2748 0.3846 0.3811 0.4204 0.4829 0.3870 0.3536 0.3122

1 1 1 1 1 1 1 1 1 1 1 1

0.4506 0.4838 0.5846 0.5904 0.6644 0.6909 0.7289 0.7746 0.8179 0.8277 0.8549 0.9368 0.93830.0384 0.0370 0.0138 0.0336 0.0367 0.0307 0.0330 0.0372 0.0232 0.0304 0.0488 0.0275 0.02950.7100 0.6700 0.7000 0.8189 0.7896 0.8062 0.8623 0.8876 0.8449 0.8678 0.9234 0.9153 0.93900.02253 0.0229 0.0251 0.0235 0.0339 0.0348 0.0356 0.0351 0.0309 0.0388 0.0391 0.0372 0.03960.01213 0.0131 0.0137 0.0100 0.0156 0.0153 0.0132 0.0118 0.0122 0.0141 0.0108 0.0108 0.00980.0331 0.0331 0.0331 0.0331 0.0331 0.0331 0.0331 0.0331 0.0331 0.0331 0.0389 0.0331 0.03890.3670 0.3972 0.4151 0.3024 0.4708 0.4630 0.3999 0.3565 0.3680 0.4269 0.2788 0.3274 0.2521

1 1 1 1 1 1 1 1 1 1 1 1

0.5790 0.5960 0.6217 0.6464 0.7447 0.8657 0.8691 0.8721 0.9045 0.9316 0.9847 1.0230 1.08200.0767 0.0283 0.0321 0.0145 0.0245 0.0121 0.0093 0.0156 0.0072 0.0144 0.0099 0.0168 0.03640.7842 0.8143 0.8425 0.8224 0.8730 0.9125 0.9326 0.9256 0.9235 0.8813 0.9089 0.9202 0.92140.03031 0.0345 0.0370 0.0334 0.0400 0.0348 0.0385 0.0421 0.0388 0.0419 0.0396 0.0440 0.04590.01408 0.0149 0.0147 0.0141 0.0143 0.0103 0.0100 0.0115 0.0107 0.0144 0.0119 0.0124 0.01290.0406 0.0406 0.0406 0.0406 0.0406 0.0406 0.0406 0.0406 0.0435 0.0406 0.0406 0.0406 0.04350.3466 0.3659 0.3616 0.3464 0.3512 0.2537 0.2464 0.2824 0.2466 0.3550 0.2939 0.3064 0.2962

1 1 1 1 1 1 1 1 1 1 1 1

0.5769 0.5919 0.6742 0.6768 0.6784 0.8338 0.8363 0.8601 0.8678 0.8856 0.8879 0.9121 0.98820.0324 0.0153 0.0324 0.0248 0.0149 0.0529 0.0443 0.0420 0.0299 0.0243 0.0127 0.0154 0.01060.6408 0.6920 0.6702 0.8007 0.8441 0.7977 0.8517 0.9170 0.9269 0.9102 0.8841 0.9175 0.92990.03835 0.0409 0.0377 0.0436 0.0553 0.0388 0.0416 0.0470 0.0539 0.0704 0.0461 0.0505 0.05340.02298 0.0227 0.0216 0.0195 0.0218 0.0175 0.0160 0.0136 0.0146 0.0211 0.0157 0.0145 0.01410.0453 0.0453 0.0453 0.0453 0.0453 0.0453 0.0453 0.0453 0.0453 0.0515 0.0453 0.0515 0.04530.5076 0.5010 0.4778 0.4302 0.4820 0.3858 0.3540 0.2992 0.3214 0.4095 0.3466 0.2814 0.3120

0.4459 0.4848 0.6120 0.6449 0.6502 0.6589 0.6869 0.7484 0.8191 0.8378 0.8512 0.8781 0.88420.0503 0.0343 0.0169 0.0121 0.0197 0.0226 0.0249 0.0265 0.0149 0.0110 0.0147 0.0278 0.02120.6986 0.7524 0.8268 0.8196 0.8361 0.8506 0.9079 0.8742 0.9142 0.9472 0.9093 0.9236 0.91160.0524 0.0480 0.0482 0.0466 0.0580 0.0492 0.0523 0.0528 0.0577 0.0543 0.0575 0.0571 0.06010.02877 0.0239 0.0201 0.0198 0.0235 0.0190 0.0159 0.0187 0.0169 0.0125 0.0173 0.0158 0.01790.0490 0.0490 0.0490 0.0490 0.0490 0.0490 0.0490 0.0490 0.0490 0.0490 0.0490 0.0490 0.05180.5868 0.4868 0.4091 0.4032 0.4788 0.3878 0.3234 0.3821 0.3449 0.2544 0.3529 0.3220 0.3453

1 1 1 1 1 1 1 1 1 1 1 1

0.5663 0.5685 0.6048 0.6368 0.6989 0.7365 0.7461 0.7755 0.8123 0.8321 0.8338 0.8868 0.89440.0831 0.0623 0.0253 0.0164 0.0167 0.0147 0.0063 0.0153 0.0045 0.0281 0.0337 0.0306 0.03360.3503 0.3700 0.7861 0.7844 0.7333 0.6313 0.8779 0.8708 0.9046 0.8660 0.8839 0.8995 0.89190.02978 0.0304 0.0341 0.0393 0.0495 0.0359 0.0365 0.0402 0.0470 0.0474 0.0447 0.0456 0.04900.02401 0.0241 0.0158 0.0182 0.0255 0.0218 0.0128 0.0144 0.0145 0.0174 0.0152 0.0145 0.01610.0465 0.0465 0.0465 0.0465 0.0465 0.0465 0.0465 0.0465 0.0465 0.0465 0.0467 0.0465 0.04650.5162 0.5183 0.3396 0.3922 0.5491 0.4690 0.2745 0.3105 0.3117 0.3730 0.3262 0.3112 0.3466

1 1 1 1 1 1 1 1 1 1 1 1

0.3768 0.3826 0.4595 0.6799 0.7064 0.7243 0.8467 0.9220 0.9564 0.9692 1.0120 1.0530 1.06300.0441 0.0239 0.0273 0.0443 0.0196 0.0574 0.0257 0.0138 0.0168 0.0128 0.0277 0.0334 0.01480.2734 0.3217 0.3434 0.5562 0.6450 0.7639 0.7830 0.7747 0.7310 0.7161 0.7984 0.8558 0.82070.02403 0.0269 0.0296 0.0330 0.0351 0.0347 0.0391 0.0403 0.0381 0.0407 0.0437 0.0432 0.04610.02048 0.0221 0.0240 0.0220 0.0209 0.0168 0.0182 0.0191 0.0198 0.0217 0.0196 0.0164 0.01950.0341 0.0341 0.0341 0.0341 0.0341 0.0341 0.0341 0.0341 0.0341 0.0341 0.0436 0.0341 0.03410.6010 0.6487 0.7048 0.6444 0.6144 0.4942 0.5341 0.5612 0.5796 0.6360 0.4500 0.4808 0.5732

1 1 1 1 1 1 1 1 1 1 1 1

0.2724 0.3200 0.3237 0.4746 0.6061 0.7194 0.7586 0.7935 0.7987 0.8390 0.9370 0.9388 0.94690.0433 0.0420 0.0240 0.0428 0.0575 0.0289 0.0276 0.0413 0.0322 0.0365 0.0206 0.0243 0.02420.1808 0.2887 0.1527 0.2102 0.4903 0.7030 0.5486 0.7944 0.7368 0.5715 0.7143 0.8191 0.78820.0212 0.0370 0.0419 0.0416 0.0455 0.0421 0.0433 0.0470 0.0490 0.0551 0.0512 0.0477 0.05400.01919 0.0312 0.0386 0.0370 0.0325 0.0229 0.0291 0.0213 0.0251 0.0361 0.0274 0.0203 0.02490.0299 0.0301 0.0299 0.0299 0.0299 0.0299 0.0299 0.0300 0.0299 0.0300 0.0307 0.0300 0.03070.6409 1.0370 1.2880 1.2340 1.0860 0.7662 0.9726 0.7115 0.8390 1.2040 0.8935 0.6781 0.8108

1 1 1 1 1 1 1 1 1 1 1 1

0.0828 0.1077 0.2610 0.4231 0.4888 0.5512 0.6108 0.7213 0.7237 0.7857 0.8590 0.9238 0.92610.0663 0.0598 0.0528 0.0240 0.0531 0.0791 0.0687 0.0348 0.0714 0.0405 0.0183 0.0085 0.00770.0419 0.2880 0.4842 0.4720 0.8177 0.6577 0.7578 0.8084 0.8059 0.6534 0.7833 0.8820 0.81030.02255 0.0272 0.0313 0.0350 0.0331 0.0295 0.0302 0.0355 0.0355 0.0425 0.0328 0.0387 0.03640.02208 0.0229 0.0225 0.0254 0.0141 0.0173 0.0149 0.0155 0.0157 0.0250 0.0153 0.0133 0.01590.0282 0.0282 0.0282 0.0281 0.0282 0.0280 0.0282 0.0281 0.0280 0.0280 0.0281 0.0315 0.02800.7823 0.8132 0.7974 0.9052 0.5004 0.6171 0.5272 0.5527 0.5598 0.8938 0.5433 0.4212 0.5674







TABLE12g:1Value=Weighted1NYSE1Market1Portfolio111111111+11111115x51Double=Sort1Test1Portfolios1Built1Using1Equal=Weighted1SecuritiesSAMPLE1STATISTICS1FOR1FOUR1SECLECTED1ESTIMATION1PERIODS1(test1portfolios11=13)





�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


39

1 1 1 1 1 1 1 1 1 1 1 1Statistics 14 15 16 17 18 19 20 21 22 23 24 25

1 1 1 1 1 1 1 1 1 1 1 1

0.9547 1.0390 1.1280 1.1440 1.1450 1.2580 1.2950 1.3200 1.3360 1.3570 1.3810 1.44600.0126 0.0203 0.0348 0.0436 0.0471 0.0291 0.0307 0.0337 0.0319 0.0621 0.0670 0.02790.7807 0.7807 0.7807 0.7807 0.7807 0.7807 0.7807 0.7807 0.7807 0.7807 0.7807 0.78070.1174 0.1332 0.0870 0.1033 0.1396 0.1458 0.1244 0.1155 0.1232 0.1385 0.1368 0.13000.0372 0.0524 0.0286 0.0269 0.0512 0.0480 0.0506 0.0321 0.0329 0.0403 0.0396 0.04690.0537 0.0598 0.0598 0.0598 0.0598 0.0598 0.0598 0.0598 0.0598 0.0598 0.0615 0.05980.6930 0.8762 0.4787 0.4505 0.8563 0.8025 0.8457 0.5373 0.5496 0.6745 0.6434 0.7839

1 1 1 1 1 1 1 1 1 1 1 1

1.1690 1.1700 1.1710 1.2380 1.2500 1.2580 1.3070 1.3130 1.3470 1.4420 1.4570 1.53600.0414 0.0090 0.0156 0.0139 0.0046 0.0021 0.0172 0.0449 0.0374 0.0285 0.0365 0.03020.9067 0.8655 0.9008 0.9297 0.9178 0.8738 0.8251 0.9191 0.8072 0.8357 0.8654 0.94430.0677 0.0834 0.0764 0.0683 0.0728 0.0894 0.0913 0.0774 0.1124 0.1097 0.1099 0.08600.0207 0.0306 0.0241 0.0181 0.0209 0.0317 0.0382 0.0220 0.0493 0.0445 0.0403 0.02030.0460 0.0483 0.0483 0.0483 0.0483 0.0483 0.0483 0.0483 0.0483 0.0483 0.0548 0.04830.4491 0.6332 0.4984 0.3751 0.4323 0.6571 0.7906 0.4555 1.0220 0.9204 0.7365 0.4201

1 1 1 1 1 1 1 1 1 1 1 1

0.9428 1.0200 1.0510 1.0640 1.0700 1.0920 1.2640 1.3590 1.5440 1.5880 1.6180 1.62700.0305 0.0013 0.0243 0.0288 0.0328 0.0379 0.0190 0.0185 0.0742 0.0750 0.0819 0.07170.8832 0.8985 0.9538 0.9281 0.9185 0.9117 0.8472 0.9135 0.9170 0.9079 0.8377 0.72250.0365 0.0407 0.0458 0.0441 0.0462 0.0453 0.0439 0.0565 0.0547 0.0568 0.0546 0.05330.0125 0.0130 0.0098 0.0118 0.0132 0.0135 0.0172 0.0166 0.0158 0.0172 0.0220 0.02810.0331 0.0389 0.0389 0.0389 0.0389 0.0389 0.0389 0.0389 0.0433 0.0389 0.0389 0.03890.3778 0.3336 0.2534 0.3046 0.3393 0.3469 0.4418 0.4274 0.3637 0.4434 0.5659 0.7225

1 1 1 1 1 1 1 1 1 1 1 1

1.0990 1.1260 1.1590 1.1740 1.1910 1.1940 1.1950 1.3250 1.3310 1.3320 1.3360 1.36200.0318 0.0232 0.0325 0.0233 0.0161 0.0125 0.0274 0.0129 0.0245 0.0255 0.0285 0.12220.9174 0.8455 0.9003 0.9024 0.8930 0.9253 0.8874 0.8998 0.8947 0.9273 0.9129 0.80210.0447 0.0501 0.0465 0.0442 0.0465 0.0555 0.0526 0.0522 0.0579 0.0545 0.0528 0.06010.0129 0.0197 0.0147 0.0138 0.0152 0.0152 0.0177 0.0165 0.0188 0.0147 0.0156 0.02670.0435 0.0434 0.0435 0.0435 0.0435 0.0435 0.0406 0.0435 0.0435 0.0435 0.0434 0.05110.2957 0.4533 0.3379 0.3174 0.3499 0.3488 0.4344 0.3799 0.4320 0.3379 0.3588 0.5225

1 1 1 1 1 1 1 1 1 1 1 1

0.9958 1.0040 1.1150 1.1350 1.1480 1.1500 1.1730 1.1780 1.1950 1.2620 1.3200 1.37200.0111 0.0114 0.0384 0.0236 0.0109 0.0163 0.0261 0.0380 0.0344 0.0482 0.0519 0.05670.9390 0.9251 0.9185 0.9378 0.9389 0.9151 0.8907 0.8945 0.9202 0.9308 0.9212 0.91410.0562 0.0653 0.0494 0.0591 0.0552 0.0679 0.0728 0.0611 0.0623 0.0645 0.0661 0.08530.0139 0.0179 0.0141 0.0147 0.0137 0.0198 0.0241 0.0199 0.0176 0.0170 0.0186 0.02500.0515 0.0515 0.0515 0.0515 0.0453 0.0515 0.0515 0.0515 0.0515 0.0515 0.0515 0.05960.2695 0.3465 0.2737 0.2861 0.3014 0.3841 0.4669 0.3853 0.3419 0.3292 0.3601 0.4196

0.9132 0.9216 1.0090 1.0380 1.0550 1.1270 1.1550 1.1720 1.2630 1.3490 1.3560 1.40100.0151 0.0218 0.0141 0.0215 0.0154 0.0290 0.0283 0.0264 0.0218 0.0451 0.0248 0.03310.9194 0.9133 0.9175 0.9225 0.9500 0.9596 0.8927 0.9319 0.9433 0.9206 0.9205 0.86740.0691 0.0720 0.0644 0.0688 0.0684 0.0759 0.0795 0.0776 0.0826 0.0825 0.0981 0.09030.0196 0.0212 0.0185 0.0192 0.0153 0.0153 0.0260 0.0203 0.0197 0.0232 0.0277 0.03290.0518 0.0518 0.0518 0.0518 0.0518 0.0518 0.0518 0.0518 0.0518 0.0518 0.0518 0.05800.3790 0.4097 0.3575 0.3699 0.2956 0.2947 0.5029 0.3913 0.3798 0.4488 0.5345 0.5670

1 1 1 1 1 1 1 1 1 1 1 1

0.9534 0.9700 0.9831 1.0010 1.0560 1.0630 1.1800 1.1830 1.2470 1.2510 1.3130 1.47700.0215 0.0199 0.0232 0.0245 0.0153 0.0425 0.0077 0.0135 0.0064 0.0303 0.0284 0.05630.9158 0.9024 0.9144 0.9238 0.9172 0.8773 0.8885 0.8873 0.9168 0.7976 0.8603 0.85760.0479 0.0484 0.0491 0.0456 0.0466 0.0491 0.0516 0.0491 0.0548 0.0532 0.0562 0.07350.0139 0.0151 0.0144 0.0126 0.0134 0.0172 0.0172 0.0165 0.0158 0.0239 0.0210 0.02770.0467 0.0467 0.0467 0.0467 0.0467 0.0467 0.0467 0.0467 0.0467 0.0467 0.0467 0.05430.2976 0.3244 0.3077 0.2696 0.2873 0.3688 0.3691 0.3531 0.3388 0.5131 0.4506 0.5106

1 1 1 1 1 1 1 1 1 1 1 1

1.0730 1.0800 1.0810 1.0980 1.1000 1.1040 1.1340 1.1710 1.1890 1.2810 1.2890 1.30700.0202 0.0201 0.0188 0.0102 0.0099 0.0130 0.0076 0.0169 0.0135 0.0278 0.0248 0.03600.8080 0.8183 0.8234 0.8309 0.7904 0.8261 0.6210 0.8839 0.8346 0.7953 0.3198 0.69490.0473 0.0509 0.0500 0.0489 0.0438 0.0521 0.0631 0.0576 0.0581 0.0654 0.0690 0.06910.0207 0.0217 0.0210 0.0201 0.0201 0.0218 0.0389 0.0196 0.0236 0.0296 0.0569 0.03810.0436 0.0436 0.0436 0.0436 0.0436 0.0436 0.0438 0.0438 0.0438 0.0438 0.0438 0.04350.4753 0.4976 0.4811 0.4603 0.4594 0.4983 0.8875 0.4481 0.5399 0.6752 1.3000 0.8767

1 1 1 1 1 1 1 1 1 1 1 1

0.9583 0.9779 1.0060 1.0280 1.1340 1.1710 1.2190 1.2580 1.3030 1.3210 1.4670 1.53800.0308 0.0324 0.0506 0.0482 0.0380 0.0361 0.0300 0.0323 0.0283 0.0208 0.0536 0.05290.8517 0.8205 0.7949 0.8326 0.8120 0.8547 0.7467 0.8685 0.8354 0.8698 0.8049 0.74490.0492 0.0557 0.0642 0.0656 0.0699 0.0627 0.0715 0.0707 0.0666 0.0767 0.0787 0.08680.0190 0.0236 0.0291 0.0269 0.0303 0.0239 0.0360 0.0257 0.0270 0.0277 0.0348 0.04380.0307 0.0300 0.0311 0.0311 0.0311 0.0311 0.0311 0.0311 0.0307 0.0311 0.0311 0.05050.6184 0.7881 0.9354 0.8642 0.9748 0.7693 1.1580 0.8256 0.8816 0.8911 1.1190 0.8680

1 1 1 1 1 1 1 1 1 1 1 1

0.9979 1.0300 1.1240 1.1390 1.1470 1.2340 1.2400 1.2700 1.2780 1.2930 1.3220 1.63100.0193 0.0207 0.0103 0.0062 0.0044 0.0190 0.0193 0.0232 0.0216 0.0240 0.0254 0.11590.8766 0.8306 0.7733 0.8334 0.8747 0.8831 0.8094 0.8624 0.8533 0.8384 0.8522 0.78390.0423 0.0499 0.0386 0.0503 0.0496 0.0476 0.0512 0.0511 0.0467 0.0506 0.0508 0.06690.0149 0.0205 0.0184 0.0205 0.0176 0.0163 0.0224 0.0190 0.0179 0.0203 0.0195 0.03110.0317 0.0315 0.0315 0.0317 0.0317 0.0317 0.0318 0.0318 0.0318 0.0318 0.0318 0.04370.4688 0.6514 0.5828 0.6473 0.5537 0.5127 0.7028 0.5956 0.5613 0.6390 0.6135 0.7125









TABLE12g:1Value=Weighted1NYSE1Market1Portfolio111111111+11111115x51Double=Sort1Test1Portfolios1Built1Using1Equal=Weighted1SecuritiesSAMPLE1STATISTICS1FOR1FOUR1SECLECTED1ESTIMATION1PERIODS1(test1portfolios114=25)111



�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


�p,t�1

s(�p,t�1)

r(Rp, Rm)2

s(ep)s(Rp)


40

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Period

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!Pane

l!A:

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

193516/68

0.0097

0.0043

11

0.0084

0.0486

0.0550

11

0.0082

0.0727

11

4.0070

1.5630

11

3.4690

0.3051

0.3016

1935145

0.0079

0.0114

11

0.0077

0.0687

0.0757

11

0.0078

0.0795

11

1.3130

1.7300

11

1.2890

0.2945

0.2914

1946155

0.0089

0.0028

11

0.0080

0.0333

0.0418

11

0.0443

0.0611

11

2.9270

0.7215

11

2.6170

0.3284

0.3196

195616/68

0.0120

10.000

71

10.0094

0.0363

0.0407

11

0.1369

0.0139

11

4.0390

10.216

01

13.1490

0.2958

0.2965

1935140

0.0052

0.0084

11

0.0051

0.0864

0.0872

11

10.080

50.0615

11

0.5032

0.8146

11

0.4956

0.2371

0.2895

1941145

0.0111

0.0150

11

0.0109

0.0388

0.0597

11

0.0950

0.1096

11

2.2130

1.9440

11

2.1710

0.3624

0.2811

1946150

0.0052

0.0034

11

0.0045

0.0377

0.0457

11

0.1602

0.0692

11

1.0660

0.5686

11

0.9293

0.4101

0.3265

1951155

0.0126

0.0022

11

0.0114

0.0281

0.0379

11

10.168

50.0462

11

3.4790

0.4400

11

3.1340

0.2466

0.2930

1956160

0.0158

10.007

71

10.0137

0.0277

0.0285

11

0.0960

0.0746

11

4.4140

12.097

01

13.8050

0.2210

0.3130

196116/68

0.0094

0.0039

11

0.0065

0.0410

0.0467

11

0.1263

10.019

71

12.1800

0.8012

11

1.4980

0.3456

0.2756

7/196812010

0.0103

0.0009

11

0.0057

0.0421

0.0573

11

0.0617

0.1131

11

5.5030

0.3614

11

3.0870

0.3260

0.2861

1970180

0.0062

0.0057

11

0.0008

0.0481

0.0614

11

0.0339

0.1379

11

1.4840

1.0690

11

0.1815

0.3167

0.2829

1980190

0.0206

10.007

91

10.0135

0.0477

0.0632

11

0.0654

0.0575

11

4.9580

11.434

01

13.2590

0.3021

0.2873

1990100

0.0096

0.0014

11

0.0055

0.0368

0.0525

11

0.0545

0.1907

11

3.0000

0.3010

11

1.7350

0.3148

0.2767

2000110

0.0076

0.0022

11

0.0055

0.0339

0.0550

11

10.016

40.1598

11

2.5780

0.4678

11

1.8820

0.3764

0.3019

1970175

0.0052

0.0017

11

0.0004

0.0541

0.0609

11

0.0268

0.0991

11

0.8114

0.2361

11

0.0602

0.3097

0.2774

1975180

0.0093

0.0127

11

0.0033

0.0422

0.0623

11

0.0286

0.1477

11

1.8690

1.7250

11

0.6678

0.3126

0.2900

1980185

0.0232

10.006

61

10.0149

0.0511

0.0607

11

0.0818

0.0294

11

3.8460

10.923

31

12.4570

0.3452

0.2898

1985190

0.0186

10.008

11

10.0130

0.0418

0.0628

11

0.0188

0.0789

11

3.7750

11.090

01

12.6380

0.2501

0.2768

1990195

0.0092

0.0014

11

0.0052

0.0363

0.0559

11

0.0779

0.2624

11

2.1570

0.2123

11

1.2380

0.2831

0.2682

1995100

0.0129

0.0002

11

0.0086

0.0372

0.0477

11

0.0690

0.1012

11

2.9480

0.0444

11

1.9810

0.3512

0.2821

2000105

0.0098

0.0015

11

0.0075

0.0357

0.0504

11

10.122

210.068

41

12.3310

0.2588

11

1.7970

0.3327

0.3018

2005110

0.0044

0.0037

11

0.0024

0.0294

0.0562

11

0.1450

0.3337

11

1.2600

0.5633

11

0.7028

0.4088

0.3008

193512010

0.0100

0.0024

11

0.0069

0.0450

0.0563

11

0.0303

0.0978

11

6.7170

1.2880

11

4.6400

0.3168

0.2930

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!B:

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

193516/68

0.0035

0.0185

10.006

71

0.0022

0.0740

0.1511

0.0650

10.0019

0.0902

0.0003

10.9582

2.4470

12.070

01

0.6047

0.0911

0.1841

1935145

0.0039

0.0226

10.005

91

0.0038

0.0887

0.1720

0.0740

10.0033

0.1702

0.0007

10.5065

1.5010

10.909

31

0.4881

0.0896

0.1868

1946155

0.0032

0.0148

10.005

31

0.0022

0.0564

0.1280

0.0531

10.0425

0.1632

0.0003

10.6164

1.2710

11.096

01

0.4329

0.1233

0.1997

195616/68

0.0035

0.0178

10.008

61

0.0009

0.0727

0.1495

0.0656

10.0135

10.056

710.000

21

0.5888

1.4570

11.602

01

0.1493

0.0666

0.1652

1935140

0.0041

0.0135

10.003

51

0.0040

0.1102

0.2006

0.0774

10.0197

0.2201

0.0009

10.3139

0.5656

10.375

71

0.3080

0.0630

0.1861

1941145

0.0037

0.0333

10.008

81

0.0035

0.0542

0.1314

0.0703

10.3537

0.0239

0.0006

10.5307

1.9640

10.964

21

0.4995

0.1211

0.1841

1946150

0.0009

0.0119

10.003

51

0.0002

0.0505

0.1206

0.0470

110.109

50.1628

0.0004

10.1327

0.7613

10.573

51

0.0307

0.1715

0.2104

1951155

0.0055

0.0178

10.007

21

0.0043

0.0621

0.1359

0.0590

10.1534

0.1568

0.0003

10.6841

1.0160

10.939

31

0.5313

0.0751

0.1773

1956160

0.0017

0.0251

10.015

61

10.000

40.0466

0.1072

0.0467

110.201

210.364

410.000

51

0.2818

1.8100

12.589

01

10.068

90.0477

0.1570

196116/68

0.0047

0.0130

10.003

91

0.0018

0.0860

0.1725

0.0755

10.0512

0.0200

0.0000

10.5176

0.7124

10.488

91

0.1933

0.0792

0.1701

7/196812010

0.0049

0.0136

10.006

61

0.0003

0.0798

0.1913

0.0929

10.0726

0.0897

0.0003

11.3790

1.6010

11.599

01

0.0958

0.1196

0.1931

1970180

10.005

70.0318

10.012

51

10.011

10.1012

0.2201

0.1012

10.1898

0.1693

0.0016

110.642

31.6610

11.423

01

11.261

00.0923

0.1762

1980190

0.0097

0.0196

10.015

11

0.0027

0.1001

0.2457

0.1248

110.090

20.0053

10.000

91

1.1140

0.9183

11.393

01

0.3047

0.1342

0.2109

1990100

0.0076

0.0091

10.005

31

0.0035

0.0563

0.1573

0.0855

10.0533

0.0171

10.000

21

1.5530

0.6674

10.707

11

0.7204

0.0993

0.1666

2000110

0.0084

10.000

70.0017

10.0063

0.0384

0.1168

0.0499

10.0333

10.011

210.000

31

2.5120

10.068

70.3981

11.9000

0.1451

0.1996

1970175

0.0033

0.0054

10.001

41

10.001

50.1058

0.2091

0.1004

10.1875

0.1753

0.0013

10.2614

0.2175

10.122

01

10.122

60.0784

0.1532

1975180

10.009

20.0535

10.019

81

10.015

20.1010

0.2318

0.1057

10.0980

0.0816

0.0008

110.776

01.9590

11.590

01

11.284

00.0999

0.1884

1980185

0.0095

0.0233

10.014

61

0.0012

0.0999

0.2309

0.1121

110.065

10.0532

0.0002

10.8060

0.8579

11.108

01

0.0992

0.1370

0.2073

1985190

0.0133

0.0105

10.012

21

0.0076

0.1003

0.2576

0.1345

110.126

610.058

110.002

31

1.1240

0.3455

10.771

41

0.6466

0.1426

0.2217

1990195

0.0056

0.0140

10.008

11

0.0016

0.0635

0.1828

0.1008

110.008

610.000

510.000

41

0.7489

0.6500

10.685

41

0.2170

0.0974

0.1615

1995100

0.0131

0.0013

10.001

21

0.0088

0.0467

0.1200

0.0621

10.1885

0.0626

0.0001

12.3820

0.0898

10.157

51

1.6100

0.1108

0.1757

2000105

0.0088

0.0039

10.001

01

0.0066

0.0353

0.0901

0.0487

10.0503

10.152

210.000

61

2.1250

0.3655

10.176

41

1.5880

0.1101

0.1716

2005110

0.0064

10.003

00.0036

10.0045

0.0400

0.1325

0.0478

10.0358

0.0479

0.0000

11.3670

10.192

80.6448

10.9573

0.1754

0.2170

193512010

0.0043

0.0157

10.006

61

0.0012

0.0773

0.1746

0.0818

10.0624

0.0895

0.0003

11.6750

2.7170

12.451

01

0.4582

0.1070

0.1896

TABLE!3b

:!Equ

al1W

eighted!NYSE!Market!Po

rtfolio!!!!!!!!!+!!!!!!!20!Single1Sort!Test!Po

rtfolios!Bu

ilt!Using!Value

1Weighted!Securities

SUMMARY

!RESULTS!FO

R!TH

E!RE

GRE

SSION

Statistics

¯ �0

¯ � 1¯ �2

¯ � 3�0�

Rf

s(�0)

s(�

1)

s(�2)

s(�3)

⇢ 0(�

0�R

f)⇢

M(�

1)

⇢0(�

2)

⇢0(�3)

t(¯ �0)

t(¯ �1)

t(¯ �2)

t(¯ �3)

t(�0�

Rf)

r2s(

r2)

Rp

=�0t+

�1t�

p+�2t�

2 p+�3ts p

(ei)

+⌘

p

41

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Period

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!Pane

l!C:

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

193516/68

0.0107

0.0070

110.055

30.0094

0.0560

0.0689

10.9425

0.0091

0.0795

110.000

43.8210

2.0350

111.174

03.3540

0.0933

0.1845

1935145

0.0080

0.0115

110.017

90.0079

0.0763

0.0890

10.8588

0.0082

0.0645

110.058

61.2030

1.4810

110.238

81.1810

0.1011

0.1922

1946155

0.0117

0.0093

110.124

40.0108

0.0420

0.0620

10.9021

0.0456

0.0638

10.0172

3.0590

1.6350

111.511

02.8100

0.1180

0.2037

195616/68

0.0122

0.0013

110.032

60.0096

0.0437

0.0520

11.0420

0.0893

0.1202

10.0309

3.4120

0.2953

110.382

92.6770

0.0668

0.1574

1935140

0.0032

0.0023

10.0544

0.0031

0.0900

0.1042

10.6782

10.072

80.1678

110.075

30.2968

0.1858

10.6755

0.2896

0.0610

0.1744

1941145

0.0138

0.0224

110.103

50.0135

0.0563

0.0659

11.0320

0.0153

10.298

61

10.039

81.8940

2.6360

110.776

21.8640

0.1485

0.2027

1946150

0.0097

0.0123

110.167

40.0090

0.0471

0.0656

10.8237

0.1974

10.018

21

0.0820

1.5950

1.4560

111.574

01.4850

0.1443

0.2002

1951155

0.0138

0.0062

110.081

40.0125

0.0365

0.0587

10.9794

10.213

50.1575

110.050

52.9190

0.8183

110.643

72.6530

0.0917

0.2055

1956160

0.0119

10.011

21

0.1215

0.0098

0.0351

0.0405

11.0900

0.0794

0.0134

110.074

92.6300

12.135

01

0.8631

2.1590

0.0476

0.1317

196116/68

0.0123

0.0095

110.135

30.0094

0.0487

0.0572

11.0020

0.0932

0.1027

10.0753

2.4010

1.5800

111.281

01.8270

0.0796

0.1719

7/196812010

0.0124

0.0050

110.082

50.0078

0.0509

0.0842

11.1370

0.0821

10.029

21

0.0355

5.4810

1.3290

111.638

03.4900

0.1127

0.1875

1970180

0.0074

0.0073

110.053

10.0020

0.0589

0.0805

11.2500

10.017

010.097

01

10.132

51.4460

1.0380

110.487

80.3830

0.0939

0.1815

1980190

0.0265

0.0033

110.206

40.0194

0.0514

0.1010

11.1800

0.1568

10.053

11

0.1226

5.9220

0.3770

112.009

04.3490

0.1096

0.1859

1990100

0.0080

0.0007

10.0263

0.0039

0.0443

0.0705

10.9101

0.0872

0.0317

110.016

72.0680

0.1091

10.3319

1.0130

0.1008

0.1690

2000110

0.0083

0.0023

110.010

60.0063

0.0474

0.0836

11.1560

0.0396

0.1210

10.1420

2.0230

0.3102

110.105

41.5240

0.1399

0.1991

1970175

0.0094

0.0129

110.213

70.0046

0.0650

0.0901

11.3780

10.017

310.184

41

10.195

71.2260

1.2120

111.316

00.6010

0.0874

0.1664

1975180

0.0074

0.0047

10.1107

0.0014

0.0523

0.0702

11.0290

10.033

510.068

91

10.097

31.2040

0.5631

10.9130

0.2330

0.0882

0.1899

1980185

0.0258

10.004

41

10.054

60.0175

0.0514

0.0949

11.0110

0.1265

0.0249

10.0521

4.2560

10.393

11

10.458

02.8810

0.1144

0.1827

1985190

0.0247

0.0061

110.247

10.0191

0.0492

0.1051

11.3290

0.1764

10.114

61

0.1512

4.2630

0.4906

111.578

03.3010

0.1044

0.1962

1990195

0.0112

0.0085

110.110

40.0072

0.0437

0.0672

10.8653

0.1590

0.0324

10.0074

2.1790

1.0770

111.082

01.4180

0.1084

0.1727

1995100

0.0087

10.006

71

0.1321

0.0044

0.0457

0.0691

10.8913

0.0493

0.0109

110.041

61.6100

10.822

61

1.2570

0.8178

0.0945

0.1694

2000105

0.0144

0.0076

110.139

70.0121

0.0504

0.0831

11.2010

0.0006

0.0954

10.3374

2.4220

0.7747

110.987

72.0390

0.1293

0.1897

2005110

0.0005

10.003

71

0.1473

10.001

40.0393

0.0794

11.0330

0.0522

0.1505

110.031

00.1086

10.397

71

1.2100

10.313

10.1494

0.2036

193512010

0.0116

0.0059

110.070

50.0085

0.0532

0.0778

11.0560

0.0431

0.0088

10.0198

6.5950

2.2720

112.016

04.8430

0.1042

0.1863

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!D:

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

193516/68

0.0053

0.0160

10.005

310.019

70.0040

0.0923

0.1556

0.0720

1.0110

0.0037

0.0593

10.000

110.076

71.1480

2.0580

11.465

010.391

20.8648

0.0963

0.2064

1935145

0.0032

0.0206

10.006

30.0129

0.0031

0.1169

0.1878

0.0902

0.9925

0.0028

0.0957

0.0000

10.159

50.3128

1.2560

10.801

80.1492

0.2988

0.0967

0.2131

1946155

0.0098

0.0115

10.001

310.105

10.0088

0.0599

0.1232

0.0492

0.8559

10.018

00.1524

0.0002

10.022

11.7890

1.0240

10.279

511.346

01.6150

0.1278

0.2205

195616/68

0.0035

0.0156

10.007

60.0200

0.0009

0.0898

0.1487

0.0697

1.1350

10.045

810.052

610.000

410.048

70.4811

1.2820

11.327

00.2160

0.1254

0.0706

0.1855

1935140

10.003

50.0150

10.009

80.1031

10.003

60.1447

0.2268

0.1047

0.9544

10.052

40.1037

10.000

110.162

210.203

30.5575

10.785

60.9099

10.207

80.0542

0.2054

1941145

0.0111

0.0272

10.002

210.093

70.0109

0.0718

0.1286

0.0699

1.0340

0.0159

0.0676

0.0000

10.159

21.1970

1.6390

10.248

610.702

11.1740

0.1471

0.2126

1946150

0.0088

0.0110

0.0004

10.140

30.0081

0.0602

0.1175

0.0459

0.7444

10.099

60.1689

0.0004

0.0283

1.1320

0.7247

0.0685

11.460

01.0450

0.1675

0.2242

1951155

0.0108

0.0120

10.002

910.070

00.0095

0.0601

0.1295

0.0526

0.9597

0.0586

0.1325

0.0001

10.073

71.3880

0.7190

10.429

710.565

01.2290

0.0881

0.2112

1956160

10.003

50.0188

10.015

40.1876

10.005

60.0598

0.1077

0.0500

1.1580

10.240

710.308

310.000

710.164

910.457

31.3530

12.389

01.2540

10.729

60.0608

0.1741

196116/68

0.0082

0.0134

10.002

310.091

70.0053

0.1052

0.1712

0.0800

1.1120

10.007

40.0140

10.000

210.009

10.7424

0.7421

10.273

710.782

40.4773

0.0771

0.1935

7/196812010

0.0090

0.0141

10.004

210.099

80.0045

0.0912

0.1951

0.0963

1.1620

0.0300

0.0722

0.0001

10.010

02.2390

1.6260

10.972

811.938

01.1170

0.1328

0.2075

1970180

10.000

20.0265

10.008

310.080

210.005

60.1174

0.2187

0.1045

1.3060

0.0655

0.1415

0.0011

10.223

810.017

51.3910

10.911

610.705

010.551

80.1015

0.1971

1980190

0.0141

0.0278

10.014

710.156

50.0071

0.1112

0.2528

0.1318

1.1990

10.061

910.001

310.001

10.1411

1.4590

1.2610

11.279

011.499

00.7318

0.1520

0.2177

1990100

0.0089

0.0011

10.000

50.0129

0.0049

0.0660

0.1628

0.0904

0.9514

0.0742

10.024

210.000

410.032

11.5560

0.0770

10.067

20.1556

0.8458

0.1189

0.1905

2000110

0.0118

10.000

40.0032

10.072

30.0097

0.0511

0.1311

0.0511

1.1680

10.092

10.0638

10.000

40.0467

2.6520

10.031

70.7284

10.710

52.1900

0.1552

0.2131

1970175

0.0125

0.0057

0.0041

10.222

50.0077

0.1274

0.2120

0.1064

1.4640

0.0276

0.1590

0.0009

10.297

00.8315

0.2287

0.3267

11.289

00.5117

0.0917

0.1711

1975180

10.008

30.0438

10.017

60.0692

10.014

30.1078

0.2285

0.1053

1.0400

0.0339

0.0549

0.0005

10.155

510.651

41.6280

11.419

00.5647

11.128

00.0996

0.2118

1980185

0.0095

0.0283

10.017

010.024

90.0012

0.1107

0.2308

0.1166

1.0710

10.073

70.0319

10.000

20.0016

0.7319

1.0410

11.235

010.197

20.0942

0.1509

0.2103

1985190

0.0174

0.0197

10.011

110.177

40.0117

0.1132

0.2708

0.1441

1.3320

10.091

810.044

410.002

60.2213

1.3030

0.6183

10.652

811.130

00.8808

0.1663

0.2303

1990195

0.0116

0.0084

10.001

010.104

50.0076

0.0764

0.1825

0.1086

0.9688

0.0632

10.043

410.000

60.0066

1.2860

0.3921

10.074

810.915

40.8451

0.1270

0.1885

1995100

0.0110

10.007

30.0012

0.0904

0.0067

0.0544

0.1324

0.0629

0.8887

0.1212

0.0123

0.0000

10.075

61.7140

10.469

40.1659

0.8635

1.0500

0.1138

0.1955

2000105

0.0161

0.0035

0.0027

10.152

90.0139

0.0516

0.1170

0.0507

1.2400

0.0698

10.020

610.000

50.3871

2.6530

0.2520

0.4466

11.046

02.2790

0.1321

0.1961

2005110

0.0044

10.003

10.0024

0.0521

0.0025

0.0471

0.1368

0.0481

1.0220

10.308

70.1235

10.000

210.258

10.7932

10.191

80.4254

0.4327

0.4443

0.1712

0.2234

193512010

0.0074

0.0149

10.004

610.064

50.0043

0.0917

0.1787

0.0864

1.0980

10.000

50.0674

0.0000

10.039

32.4340

2.5170

11.621

011.774

01.4100

0.1167

0.2077

TABLE!3b

:!Equ

al1W


rtfolio!!!!!!!!!+!!!!!!!20!Single1Sort!Test!Po

rtfolios!Bu

ilt!Using!Value


SUMMARY

!RESULTS!FO

R!TH

E!RE

GRE

SSION!(con

t.)

Statistics

¯ �0

¯ � 1¯ �2

¯ � 3�0�

Rf

s(�0)

s(�

1)

s(�2)

s(�3)

⇢ 0(�

0�R

f)⇢

M(�

1)

⇢0(�

2)

⇢0(�3)

t(¯ �0)

t(¯ �1)

t(¯ �2)

t(¯ �3)

t(�0�

Rf)

r2s(

r2)

Rp

=�0t+�1t�

p+�2t�

2 p+

�3ts p

(ei)

+⌘

p

42

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Perio

d!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!A:

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

193516/68

0.0077

0.0053

11

0.0064

0.0394

0.0519

11

0.0061

10.011

41

13.9190

2.0330

11

3.2510

0.3051

0.3016

1935145

0.0083

0.0084

11

0.0082

0.0545

0.0686

11

0.0082

10.111

71

11.7500

1.4060

11

1.7200

0.2945

0.2914

1946155

0.0078

0.0029

11

0.0069

0.0259

0.0373

11

0.1394

0.0682

11

3.3180

0.8582

11

2.9200

0.3284

0.3196

195616/68

0.0071

0.0044

11

0.0045

0.0324

0.0446

11

0.2607

0.1452

11

2.6770

1.2010

11

1.6840

0.2958

0.2965

1935140

0.0082

0.0038

11

0.0081

0.0683

0.0819

11

0.0997

10.194

81

11.0150

0.3957

11

1.0050

0.2371

0.2895

1941145

0.0085

0.0139

11

0.0082

0.0317

0.0484

11

0.1363

0.1414

11

2.0620

2.2150

11

2.0100

0.3624

0.2811

1946150

0.0044

0.0028

11

0.0038

0.0312

0.0423

11

0.2255

0.0334

11

1.1000

0.5097

11

0.9342

0.4101

0.3265

1951155

0.0113

0.0031

11

0.0100

0.0188

0.0319

11

10.055

30.0701

11

4.6360

0.7435

11

4.1280

0.2466

0.2930

1956160

0.0154

10.006

81

10.0133

0.0208

0.0406

11

0.1759

0.1503

11

5.7230

11.299

01

14.9340

0.2210

0.3130

196116/68

0.0015

0.0118

11

10.001

40.0372

0.0458

11

0.2184

0.0865

11

0.3885

2.4530

11

10.359

80.3456

0.2756

7/196812010

0.0082

0.0029

11

0.0037

0.0385

0.0575

11

0.1320

0.1811

11

4.8140

1.1350

11

2.1630

0.3260

0.2861

1970180

0.0014

0.0092

11

10.004

00.0423

0.0633

11

0.2181

0.1851

11

0.3892

1.6700

11

11.098

00.3167

0.2829

1980190

0.0184

10.005

01

10.0113

0.0424

0.0619

11

0.0569

0.2157

11

4.9720

10.919

71

13.0840

0.3021

0.2873

1990100

0.0082

0.0031

11

0.0042

0.0392

0.0579

11

0.1096

0.1778

11

2.4180

0.6192

11

1.2270

0.3148

0.2767

2000110

0.0088

0.0008

11

0.0067

0.0308

0.0518

11

0.0267

0.1156

11

3.2810

0.1806

11

2.5170

0.3764

0.3019

1970175

0.0045

0.0009

11

10.000

30.0418

0.0587

11

0.1852

0.1544

11

0.9150

0.1332

11

10.057

60.3097

0.2774

1975180

10.000

50.0209

11

10.006

50.0436

0.0680

11

0.2443

0.2274

11

10.096

82.6040

11

11.282

00.3126

0.2900

1980185

0.0193

10.001

81

10.0110

0.0427

0.0578

11

0.0936

0.1761

11

3.8410

10.260

21

12.2020

0.3452

0.2898

1985190

0.0192

10.008

01

10.0135

0.0406

0.0631

11

0.0335

0.2430

11

4.0030

11.076

01

12.8430

0.2501

0.2768

1990195

0.0080

0.0030

11

0.0041

0.0394

0.0562

11

0.1931

0.2868

11

1.7320

0.4523

11

0.8818

0.2831

0.2682

1995100

0.0110

0.0026

11

0.0067

0.0382

0.0575

11

0.0474

0.0713

11

2.4320

0.3790

11

1.4900

0.3512

0.2821

2000105

0.0113

10.000

11

10.0091

0.0308

0.0527

11

10.086

610.040

01

13.1210

10.010

41

12.5070

0.3327

0.3018

2005110

0.0059

0.0017

11

0.0039

0.0294

0.0473

11

0.1521

0.2953

11

1.6990

0.3031

11

1.1390

0.4088

0.3008

193512010

0.0080

0.0039

11

0.0049

0.0389

0.0551

11

0.1417

0.1083

11

6.2010

2.1570

11

3.7900

0.3168

0.2930

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!B:

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

193516/68

0.0029

0.0154

10.004

71

0.0016

0.0584

0.1102

0.0441

10.0012

0.0632

0.0002

11.0000

2.8040

12.126

01

0.5521

0.3076

0.2954

1935145

0.0097

0.0061

0.0009

10.0095

0.0653

0.1093

0.0386

10.0095

10.162

310.000

11

1.6990

0.6402

0.2552

11.6750

0.2999

0.3069

1946155

10.001

30.0191

10.006

31

10.002

20.0401

0.0840

0.0289

10.0684

0.0004

0.0000

110.353

32.4930

12.393

01

10.611

40.3532

0.3083

195616/68

0.0004

0.0206

10.008

21

10.002

20.0640

0.1282

0.0567

10.3073

0.2250

0.0007

10.0707

1.9690

11.775

01

10.427

60.2779

0.2711

1935140

0.0086

0.0032

0.0003

10.0085

0.0717

0.1299

0.0378

10.0481

10.190

210.000

31

1.0110

0.2077

0.0651

11.0020

0.2437

0.3062

1941145

0.0110

0.0096

0.0015

10.0108

0.0573

0.0792

0.0397

10.0832

10.083

00.0001

11.4830

0.9345

0.2987

11.4540

0.3665

0.2967

1946150

10.004

30.0171

10.005

11

10.005

00.0456

0.0891

0.0250

10.1131

0.0714

0.0001

110.729

11.4840

11.572

01

10.841

20.4167

0.3256

1951155

0.0017

0.0212

10.007

61

0.0005

0.0337

0.0792

0.0325

110.018

410.105

60.0000

10.3925

2.0700

11.800

01

0.1112

0.2896

0.2784

1956160

0.0067

0.0153

10.011

41

0.0046

0.0312

0.0780

0.0398

10.2253

0.0774

0.0005

11.6570

1.5210

12.220

01

1.1290

0.2579

0.2857

196116/68

10.003

80.0241

10.006

11

10.006

80.0786

0.1531

0.0657

10.3058

0.2487

0.0008

110.461

91.4960

10.879

21

10.816

80.2912

0.2617

7/196812010

0.0058

0.0092

10.003

11

0.0013

0.0715

0.1438

0.0621

10.0434

0.0081

10.000

11

1.8360

1.4470

11.145

01

0.4037

0.3335

0.2866

1970180

0.0067

10.000

30.0039

10.0012

0.1024

0.1829

0.0747

10.0131

10.062

110.000

31

0.7511

10.016

20.5965

10.1386

0.3419

0.2726

1980190

0.0066

0.0239

10.014

61

10.000

40.0826

0.1655

0.0614

10.0533

0.0631

0.0000

10.9230

1.6570

12.732

01

10.058

50.3453

0.3015

1990100

0.0092

10.000

20.0023

10.0051

0.0575

0.1386

0.0714

10.1622

0.0939

0.0002

11.8430

10.020

70.3700

11.0280

0.3216

0.2688

2000110

0.0071

0.0056

10.002

31

0.0051

0.0353

0.0935

0.0450

10.1136

10.007

410.000

31

2.3230

0.6849

10.594

71

1.6520

0.3473

0.3022

1970175

10.000

30.0108

10.004

51

10.005

10.1050

0.1872

0.0812

110.033

910.124

110.000

71

10.023

30.4913

10.466

31

10.410

00.3195

0.2616

1975180

0.0148

10.007

00.0113

10.0088

0.1053

0.1883

0.0769

10.0387

10.027

010.000

21

1.1910

10.313

41.2470

10.7092

0.3639

0.2832

1980185

0.0142

0.0096

10.005

21

0.0059

0.0873

0.1574

0.0553

10.1045

0.1200

0.0001

11.3810

0.5182

10.794

91

0.5756

0.3821

0.2928

1985190

0.0007

0.0380

10.023

71

10.004

90.0744

0.1670

0.0637

110.046

010.018

610.000

11

0.0828

1.9310

13.155

01

10.561

40.3005

0.3112

1990195

0.0078

0.0035

0.0001

10.0038

0.0627

0.1415

0.0758

10.2046

0.1084

0.0006

11.0550

0.2088

0.0118

10.5164

0.2920

0.2628

1995100

0.0106

0.0022

0.0011

10.0063

0.0504

0.1309

0.0630

10.0712

0.0733

10.000

11

1.7810

0.1438

0.1435

11.0630

0.3752

0.2694

2000105

0.0099

0.0044

10.002

51

0.0077

0.0339

0.0935

0.0568

10.0997

10.099

910.000

61

2.4850

0.4021

10.368

61

1.9260

0.3231

0.2779

2005110

0.0035

0.0076

10.002

51

0.0016

0.0359

0.0877

0.0235

10.1275

0.0922

0.0000

10.8340

0.7322

10.908

91

0.3742

0.3497

0.3180

193512010

0.0045

0.0120

10.003

81

0.0014

0.0661

0.1301

0.0549

10.0896

0.0261

0.0000

12.0740

2.7730

12.102

01

0.6514

0.3221

0.2906

TABLE!3c:!V

alue

1Weighted!NYSE!Market!P


ortfolios!B

uilt!Usin

g!Equal1W

eighted!Securities

SUMMAR

Y!RE

SULTS!FO

R!TH

E!RE

GRESSION

Statistics

¯ �0

¯ � 1¯ �2

¯ � 3�0�

Rf

s(�0)

s(�

1)

s(�2)

s(�3)

⇢ 0(�

0�R

f)⇢

M(�

1)

⇢0(�

2)

⇢0(�3)

t(¯ �0)

t(¯ �1)

t(¯ �2)

t(¯ �3)

t(�0�

Rf)

r2s(

r2)

Rp

=�0t+�1t�

p+�2t�

2 p+

�3ts p

(ei)

+⌘

p

43

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Perio

d!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!C:

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

193516/68

0.0093

0.0082

110.072

90.0080

0.0499

0.0518

10.7504

0.0077

10.095

91

0.0121

3.7340

3.1680

111.946

03.2090

0.3098

0.2988

1935145

0.0082

0.0077

10.0088

0.0080

0.0709

0.0621

10.7051

0.0082

10.233

61

10.077

61.3220

1.4220

10.1422

1.2990

0.2995

0.3053

1946155

0.0095

0.0085

110.122

00.0085

0.0306

0.0440

10.6012

0.0642

10.103

81

10.044

93.3890

2.1300

112.224

03.0520

0.3600

0.3161

195616/68

0.0102

0.0083

110.104

90.0076

0.0395

0.0480

10.8834

0.1732

0.1148

10.1328

3.1540

2.1280

111.455

02.3370

0.2785

0.2747

1935140

0.0098

0.0064

110.052

10.0097

0.0861

0.0740

10.5839

10.043

810.257

31

10.075

30.9567

0.7243

110.751

80.9490

0.2438

0.3067

1941145

0.0063

0.0093

10.0808

0.0061

0.0477

0.0445

10.8254

0.0857

10.144

61

10.054

01.0260

1.6190

10.7580

0.9902

0.3655

0.2927

1946150

0.0057

0.0093

110.125

20.0050

0.0346

0.0487

10.5616

0.1704

10.110

21

10.021

41.2710

1.4760

111.727

01.1210

0.4294

0.3233

1951155

0.0133

0.0078

110.118

90.0120

0.0257

0.0391

10.6431

10.092

910.147

31

10.059

33.9930

1.5490

111.431

03.6220

0.2906

0.2953

1956160

0.0196

0.0010

110.189

60.0175

0.0311

0.0413

10.9049

0.2621

0.0764

10.2536

4.8850

0.1827

111.623

04.3660

0.2512

0.2898

196116/68

0.0039

0.0133

110.048

50.0009

0.0432

0.0517

10.8692

0.0806

0.1165

10.0536

0.8482

2.4340

110.529

30.2021

0.2967

0.2642

7/196812010

0.0079

0.0003

10.0376

0.0033

0.0460

0.0713

10.8925

0.0840

0.0419

110.016

43.8640

0.0992

10.9504

1.6440

0.3182

0.2816

1970180

10.001

110.002

01

0.1857

10.006

50.0497

0.0731

11.0340

0.1503

10.055

11

0.0229

10.251

710.308

31

2.0630

11.522

00.3404

0.2749

1980190

0.0198

10.001

51

10.064

70.0128

0.0467

0.0852

10.7812

10.023

40.0310

110.114

34.8770

10.199

61

10.950

93.1560

0.3152

0.2885

1990100

0.0062

10.000

91

0.0708

0.0021

0.0434

0.0606

10.6678

0.0822

0.1050

10.0365

1.6360

10.172

31

1.2190

0.5562

0.3012

0.2732

2000110

0.0078

10.000

41

0.0303

0.0057

0.0447

0.0762

10.9884

0.0409

0.0900

110.029

52.0070

10.064

11

0.3521

1.4710

0.3218

0.2908

1970175

0.0016

10.002

21

0.0916

10.003

20.0531

0.0640

11.1350

0.0873

0.0345

110.002

40.2582

10.297

71

0.6851

10.506

80.3171

0.2694

1975180

10.003

20.0036

10.2652

10.009

20.0468

0.0826

11.0050

0.2568

10.104

81

0.1128

10.577

70.3718

12.2390

11.688

00.3666

0.2818

1980185

0.0190

10.008

01

0.0838

0.0107

0.0471

0.0830

10.8482

0.0404

10.052

31

10.140

93.4270

10.822

31

0.8380

1.9360

0.3512

0.2860

1985190

0.0222

0.0047

110.203

10.0166

0.0442

0.0851

10.6847

10.076

10.0843

110.094

04.2560

0.4679

112.517

03.1910

0.2663

0.2867

1990195

0.0076

0.0001

10.0411

0.0036

0.0410

0.0537

10.5840

0.1750

0.2369

10.0699

1.5690

0.0121

10.5964

0.7514

0.2841

0.2654

1995100

0.0076

10.001

81

0.0872

0.0033

0.0445

0.0646

10.7058

0.0219

0.0192

110.007

41.4470

10.230

41

1.0480

0.6347

0.3330

0.2780

2000105

0.0098

10.002

81

0.0539

0.0075

0.0377

0.0735

10.8449

10.174

810.026

31

10.064

52.1990

10.326

41

0.5414

1.6870

0.2820

0.2821

2005110

0.0050

0.0015

10.0179

0.0031

0.0486

0.0741

11.0730

0.1728

0.2041

10.0247

0.8778

0.1733

10.1418

0.5368

0.3397

0.2917

193512010

0.0085

0.0038

110.011

10.0054

0.0478

0.0636

10.8343

0.0651

0.0059

110.003

15.3760

1.7970

110.400

53.4090

0.3145

0.2892

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!D:

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

193516/68

0.0050

0.0147

10.003

710.038

30.0037

0.0764

0.1110

0.0455

0.7757

0.0032

0.0791

0.0002

10.026

61.3180

2.6470

11.635

010.987

90.9757

0.3195

0.3043

1935145

0.0075

0.0073

10.000

40.0352

0.0073

0.0979

0.1127

0.0412

0.7479

0.0077

10.097

010.000

110.104

40.8713

0.7402

10.107

40.5385

0.8547

0.3115

0.3125

1946155

0.0040

0.0163

10.003

610.090

90.0030

0.0475

0.0819

0.0293

0.6156

0.0351

0.0570

0.0001

10.034

90.9184

2.1850

11.353

011.618

00.6998

0.3661

0.3216

195616/68

0.0038

0.0198

10.006

710.060

30.0011

0.0742

0.1288

0.0581

0.9040

0.2008

0.2049

0.0005

0.0467

0.6191

1.8830

11.413

010.817

20.1887

0.2891

0.2793

1935140

0.0135

0.0009

0.0018

10.043

90.0134

0.1101

0.1383

0.0433

0.6429

0.0255

10.085

610.000

110.046

61.0330

0.0529

0.3571

10.575

41.0270

0.2489

0.3162

1941145

0.0003

0.0149

10.003

00.1288

0.0001

0.0816

0.0721

0.0387

0.8519

10.108

310.178

810.000

210.133

10.0298

1.5990

10.603

11.1710

0.0088

0.3856

0.2937

1946150

0.0023

0.0141

10.002

110.108

60.0016

0.0575

0.0905

0.0273

0.5920

0.1327

0.1441

0.0001

10.013

50.3071

1.2060

10.599

711.420

00.2172

0.4313

0.3321

1951155

0.0057

0.0186

10.005

110.073

20.0045

0.0353

0.0730

0.0313

0.6428

10.115

110.088

40.0000

10.039

31.2490

1.9720

11.268

010.882

60.9786

0.3009

0.2995

1956160

0.0107

0.0150

10.009

410.091

80.0085

0.0443

0.0817

0.0406

0.9351

10.156

90.0006

0.0000

0.0093

1.8640

1.4210

11.790

010.760

41.4970

0.2525

0.2952

196116/68

10.000

90.0230

10.004

910.039

310.003

80.0887

0.1527

0.0674

0.8874

0.2519

0.2417

0.0008

0.0716

10.091

31.4300

10.691

110.420

510.405

70.3135

0.2671

7/196812010

10.001

30.0142

10.008

20.1044

10.005

80.0892

0.1520

0.0698

0.9407

0.1055

0.0150

10.000

10.0326

10.325

82.1070

12.654

02.5060

11.474

00.3535

0.2922

1970180

10.014

60.0160

10.009

60.2805

10.020

10.1302

0.1923

0.0865

1.1690

0.1672

10.006

00.0003

0.2879

11.290

00.9540

11.271

02.7560

11.775

00.3733

0.2791

1980190

0.0037

0.0227

10.016

40.0778

10.003

40.0947

0.1759

0.0761

0.7946

0.0490

0.0549

10.000

110.109

00.4492

1.4810

12.475

01.1250

10.408

60.3478

0.3097

1990100

0.0057

0.0007

10.000

50.0671

0.0016

0.0713

0.1488

0.0806

0.7340

0.0881

0.0293

10.000

610.018

30.9185

0.0559

10.064

41.0500

0.2604

0.3355

0.2752

2000110

0.0055

0.0050

10.002

90.0385

0.0034

0.0477

0.1038

0.0448

0.9713

0.0131

0.0391

10.000

410.069

91.3200

0.5516

10.737

00.4554

0.8175

0.3704

0.3019

1970175

10.023

00.0297

10.016

50.2600

10.027

80.1336

0.1926

0.0880

1.1810

0.1943

10.030

30.0007

0.3707

11.460

01.3060

11.596

01.8680

11.763

00.3529

0.2691

1975180

10.001

40.0029

10.000

90.2605

10.007

40.1303

0.1979

0.0906

1.1770

0.1023

10.043

210.000

70.3063

10.093

50.1227

10.083

41.8780

10.486

00.3944

0.2952

1980185

0.0063

0.0078

10.009

70.1904

10.002

10.0889

0.1583

0.0554

0.7527

0.1994

0.1145

0.0004

10.042

00.5981

0.4188

11.482

02.1460

10.197

40.3852

0.3022

1985190

0.0019

0.0371

10.023

010.015

510.003

70.0966

0.1850

0.0886

0.7998

10.089

810.015

610.000

610.167

40.1687

1.7010

12.200

010.164

110.327

20.3009

0.3151

1990195

0.0049

0.0068

10.003

60.0457

0.0009

0.0812

0.1584

0.0907

0.7231

0.0816

0.0292

10.000

90.0361

0.5110

0.3661

10.334

00.5362

0.0957

0.3112

0.2743

1995100

0.0069

10.000

10.0000

0.0832

0.0026

0.0568

0.1325

0.0639

0.6991

0.0818

0.0256

10.000

210.074

11.0300

10.005

20.0063

1.0100

0.3919

0.3822

0.2709

2000105

0.0077

0.0033

10.003

40.0560

0.0055

0.0392

0.1024

0.0565

0.8238

10.072

210.057

510.000

710.077

41.6680

0.2762

10.513

30.5763

1.1780

0.3359

0.2828

2005110

0.0017

0.0068

10.002

60.0386

10.000

20.0534

0.0989

0.0235

1.0610

0.0732

0.1399

0.0000

10.033

40.2771

0.5825

10.953

10.3091

10.031

40.3819

0.3110

193512010

0.0015

0.0144

10.006

20.0416

10.001

60.0839

0.1355

0.0604

0.8743

0.0936

0.0333

0.0000

0.0073

0.5377

3.2090

13.115

01.4360

10.582

60.3385

0.2979

TABLE!3c:!V

alue



ortfolios!B

uilt!Usin

g!Equal1W

eighted!Securities

SUMMAR

Y!RE

SULTS!FO

R!TH

E!RE

GRESSION!(con

t.)

Statistics

¯ �0

¯ � 1¯ �2

¯ � 3�0�

Rf

s(�0)

s(�

1)

s(�2)

s(�3)

⇢ 0(�

0�R

f)⇢

M(�

1)

⇢0(�

2)

⇢0(�3)

t(¯ �0)

t(¯ �1)

t(¯ �2)

t(¯ �3)

t(�0�

Rf)

r2s(

r2)

Rp

=�0t+

�1t�

p+�2t�

2 p+

�3ts p

(ei)

+⌘

p

44

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Perio

d!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!A:

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

193516/68

0.0096

0.0026

11

0.0083

0.0528

0.0472

11

0.0080

0.0339

11

3.6250

1.1050

11

3.1330

0.3051

0.3016

1935145

0.0061

0.0088

11

0.0060

0.0730

0.0586

11

0.0060

10.024

41

10.9563

1.7170

11

0.9339

0.2945

0.2914

1946155

0.0082

0.0031

11

0.0072

0.0376

0.0396

11

0.0480

0.0870

11

2.3780

0.8448

11

2.1030

0.3284

0.3196

195616/68

0.0137

10.003

11

10.0111

0.0410

0.0410

11

0.2004

0.0572

11

4.0900

10.941

01

13.3090

0.2958

0.2965

1935140

0.0057

0.0049

11

0.0056

0.0900

0.0676

11

0.0153

10.068

01

10.5316

0.6171

11

0.5243

0.2371

0.2895

1941145

0.0066

0.0133

11

0.0064

0.0461

0.0458

11

10.008

80.0616

11

1.1070

2.2520

11

1.0710

0.3624

0.2811

1946150

0.0028

0.0048

11

0.0022

0.0446

0.0454

11

0.1849

0.0751

11

0.4909

0.8178

11

0.3751

0.4101

0.3265

1951155

0.0135

0.0013

11

0.0123

0.0284

0.0331

11

10.289

90.0947

11

3.6850

0.3079

11

3.3470

0.2466

0.2930

1956160

0.0148

10.007

11

10.0127

0.0262

0.0322

11

0.2778

0.0337

11

4.3790

11.694

01

13.7420

0.2210

0.3130

196116/68

0.0130

10.000

51

10.0100

0.0486

0.0459

11

0.1801

0.0581

11

2.5320

10.112

71

11.9590

0.3456

0.2756

7/196812010

0.0110

0.0000

11

0.0064

0.0451

0.0544

11

0.0764

0.1031

11

5.4830

10.006

21

13.2250

0.3260

0.2861

1970180

0.0071

0.0043

11

0.0016

0.0531

0.0552

11

0.1025

0.2262

11

1.5290

0.8900

11

0.3495

0.3167

0.2829

1980190

0.0193

10.006

11

10.0123

0.0481

0.0640

11

0.0116

0.0786

11

4.6110

11.101

01

12.9360

0.3021

0.2873

1990100

0.0096

0.0016

11

0.0055

0.0377

0.0526

11

0.0824

0.0614

11

2.9220

0.3412

11

1.6870

0.3148

0.2767

2000110

0.0111

10.002

31

10.0090

0.0355

0.0488

11

0.0163

0.0983

11

3.5730

10.552

41

12.9080

0.3764

0.3019

1970175

0.0085

10.001

41

10.0038

0.0622

0.0520

11

0.1359

0.2678

11

1.1650

10.226

71

10.5120

0.3097

0.2774

1975180

0.0074

0.0125

11

0.0014

0.0482

0.0569

11

0.0137

0.1922

11

1.2970

1.8680

11

0.2428

0.3126

0.2900

1980185

0.0216

10.004

81

10.0133

0.0486

0.0591

11

0.0023

0.0895

11

3.7750

10.684

61

12.3200

0.3452

0.2898

1985190

0.0204

10.009

01

10.0147

0.0456

0.0649

11

0.0302

0.0694

11

3.7920

11.173

01

12.7540

0.2501

0.2768

1990195

0.0116

10.000

81

10.0076

0.0349

0.0492

11

0.0817

0.0415

11

2.8270

10.131

71

11.8740

0.2831

0.2682

1995100

0.0113

0.0019

11

0.0070

0.0411

0.0547

11

0.1258

0.0971

11

2.3220

0.3004

11

1.4450

0.3512

0.2821

2000105

0.0162

10.004

91

10.0139

0.0323

0.0457

11

10.099

710.064

51

14.2510

10.904

71

13.6590

0.3327

0.3018

2005110

0.0058

0.0002

11

0.0038

0.0362

0.0489

11

0.0795

0.2202

11

1.3580

0.0431

11

0.9031

0.4088

0.3008

193512010

0.0103

0.0011

11

0.0072

0.0486

0.0514

11

0.0679

0.0787

11

6.4180

0.6693

11

4.4960

0.3168

0.2930

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!B:

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

193516/68

0.0055

0.0111

10.003

91

0.0042

0.0807

0.1557

0.0661

10.0041

10.068

310.000

41

1.3760

1.4250

11.187

01

1.0530

0.0844

0.1824

1935145

0.0042

0.0115

10.000

71

0.0040

0.0940

0.1546

0.0515

10.0040

10.058

410.000

11

0.5088

0.8497

10.162

11

0.4914

0.0852

0.1790

1946155

0.0051

0.0090

10.002

51

0.0041

0.0648

0.1247

0.0496

110.150

610.131

410.000

61

0.8584

0.7925

10.556

71

0.6988

0.1164

0.2132

195616/68

0.0071

0.0124

10.007

81

0.0045

0.0802

0.1782

0.0861

10.0462

10.053

210.000

51

1.0880

0.8495

11.112

01

0.6892

0.0582

0.1535

1935140

0.0049

0.0064

10.000

51

0.0049

0.1109

0.1771

0.0557

10.0138

10.079

710.000

41

0.3759

0.3037

10.080

51

0.3700

0.0725

0.1717

1941145

0.0033

0.0175

10.001

01

0.0030

0.0697

0.1240

0.0465

10.1272

10.021

20.0001

10.3629

1.0940

10.160

41

0.3385

0.1003

0.1875

1946150

0.0020

0.0055

10.000

11

0.0014

0.0611

0.1019

0.0344

110.160

810.026

40.0000

10.2573

0.4203

10.014

41

0.1730

0.1494

0.2207

1951155

0.0081

0.0125

10.005

01

0.0069

0.0686

0.1447

0.0613

110.131

310.193

610.001

21

0.9170

0.6695

10.628

21

0.7788

0.0834

0.2019

1956160

0.0017

0.0287

10.019

81

10.000

40.0574

0.1461

0.0721

110.110

110.244

910.000

61

0.2319

1.5240

12.124

01

10.052

60.0170

0.1205

196116/68

0.0107

0.0015

0.0002

10.0078

0.0924

0.1968

0.0938

10.0732

10.001

910.000

51

1.1000

0.0699

0.0153

10.7983

0.0856

0.1671

7/196812010

0.0078

0.0084

10.004

51

0.0032

0.0960

0.1920

0.0869

10.1216

0.0940

0.0003

11.8270

0.9822

11.169

01

0.7603

0.0942

0.1787

1970180

0.0015

0.0148

10.004

41

10.003

90.1504

0.2683

0.1061

10.1876

0.1559

0.0018

10.1167

0.6351

10.481

31

10.300

20.0822

0.1706

1980190

0.0124

0.0119

10.009

71

0.0053

0.0912

0.1970

0.0896

10.0196

0.0867

0.0003

11.5580

0.6948

11.248

01

0.6718

0.0945

0.1798

1990100

0.0118

10.004

20.0029

10.0078

0.0578

0.1585

0.0920

10.0041

10.063

910.000

81

2.3530

10.305

10.3639

11.5410

0.0789

0.1637

2000110

0.0057

0.0164

10.011

41

0.0036

0.0411

0.1036

0.0516

10.0218

0.0069

0.0001

11.5850

1.8170

12.532

01

1.0070

0.1176

0.1913

1970175

0.0106

10.004

70.0012

10.0058

0.1668

0.2886

0.1187

10.2909

0.2477

0.0034

10.5380

10.138

40.0870

10.2939

0.0786

0.1660

1975180

10.000

30.0263

10.005

51

10.006

30.1354

0.2480

0.0945

110.039

910.025

110.000

51

10.015

80.8987

10.496

31

10.392

30.0808

0.1699

1980185

0.0152

0.0092

10.006

51

0.0069

0.1017

0.2046

0.0875

110.091

80.0092

10.000

31

1.2670

0.3820

10.633

71

0.5752

0.1087

0.1790

1985190

0.0103

0.0179

10.014

71

0.0046

0.0803

0.1942

0.0936

10.1986

0.1565

0.0008

11.0870

0.7804

11.332

01

0.4914

0.0802

0.1765

1990195

0.0105

0.0027

10.002

11

0.0066

0.0625

0.1624

0.0943

110.137

910.201

710.001

81

1.4300

0.1406

10.188

11

0.8907

0.0733

0.1434

1995100

0.0164

10.011

90.0074

10.0121

0.0525

0.1500

0.0849

10.1888

0.0579

0.0000

12.6450

10.672

80.7360

11.9530

0.0895

0.1844

2000105

0.0043

0.0342

10.022

81

0.0020

0.0398

0.1025

0.0617

10.0064

10.033

10.0003

10.9113

2.8310

13.133

01

0.4289

0.0908

0.1647

2005110

0.0063

10.000

70.0003

10.0044

0.0411

0.0961

0.0299

10.0343

10.037

010.000

11

1.2990

10.066

00.0756

10.9008

0.1436

0.2114

193512010

0.0068

0.0096

10.004

21

0.0037

0.0895

0.1769

0.0784

10.0808

0.0389

0.0000

12.2890

1.6300

11.633

01

1.2390

0.0899

0.1803

TABLE!3d

:!Value



ortfolios!B

uilt!Usin

g!Equal1W

eighted!Securities

SUMMAR

Y!RE

SULTS!FO

R!TH

E!RE

GRESSION

Statistics

¯ �0

¯ � 1¯ �2

¯ � 3�0�

Rf

s(�0)

s(�

1)

s(�2)

s(�3)

⇢ 0(�

0�R

f)⇢

M(�

1)

⇢0(�

2)

⇢0(�3)

t(¯ �0)

t(¯ �1)

t(¯ �2)

t(¯ �3)

t(�0�

Rf)

r2s(

r2)

Rp

=�0t+

�1t�

p+�2t�

2 p+�3ts p

(ei)

+⌘

p

45

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Perio

d!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!C:

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

193516/68

0.0114

0.0062

110.081

40.0101

0.0586

0.0548

10.8072

0.0099

0.0182

110.099

93.8840

2.2530

112.019

03.4420

0.0905

0.1856

1935145

0.0075

0.0107

110.030

70.0074

0.0781

0.0626

10.4746

0.0075

10.012

91

10.015

31.1040

1.9540

110.740

51.0830

0.0811

0.1719

1946155

0.0091

0.0072

110.096

10.0082

0.0395

0.0515

10.8120

0.0276

0.0790

110.103

32.5360

1.5400

111.297

02.2740

0.1247

0.2208

195616/68

0.0165

0.0014

110.113

80.0139

0.0510

0.0498

11.0110

0.0351

10.006

21

10.172

73.9550

0.3323

111.378

03.3300

0.0715

0.1624

1935140

0.0077

0.0062

110.015

50.0077

0.0952

0.0689

10.4469

10.059

710.000

81

10.009

50.6850

0.7563

110.293

00.6781

0.0678

0.1584

1941145

0.0073

0.0160

110.048

70.0071

0.0518

0.0543

10.5087

10.079

610.061

41

10.022

71.0900

2.2860

110.740

81.0580

0.0969

0.1867

1946150

0.0026

0.0073

110.048

70.0020

0.0437

0.0568

10.7199

0.2025

0.0494

110.044

90.4671

0.9939

110.524

10.3490

0.1641

0.2247

1951155

0.0156

0.0072

110.143

60.0144

0.0339

0.0462

10.8983

10.257

10.1264

110.171

13.5780

1.2080

111.238

03.2950

0.0852

0.2114

1956160

0.0187

10.001

21

10.146

80.0166

0.0334

0.0514

11.2910

10.141

610.044

51

10.256

84.3450

10.184

51

10.880

83.8590

0.0575

0.1427

196116/68

0.0150

0.0031

110.091

80.0121

0.0602

0.0490

10.7780

0.0624

0.0164

110.113

62.3660

0.5947

111.119

01.9030

0.0807

0.1744

7/196812010

0.0103

10.002

01

0.0378

0.0058

0.0536

0.0637

10.8938

0.0721

0.0143

110.038

24.3380

10.704

41

0.9561

2.4330

0.0892

0.1666

1970180

0.0040

10.004

01

0.1644

10.001

50.0638

0.0685

11.1850

0.1083

0.0348

110.007

20.7198

10.675

71

1.5930

10.263

60.0834

0.1639

1980190

0.0189

10.006

71

0.0131

0.0119

0.0507

0.0756

10.7363

0.0154

10.020

91

10.118

14.2880

11.013

01

0.2039

2.6980

0.0836

0.1788

1990100

0.0097

0.0026

110.016

90.0056

0.0481

0.0553

10.6540

0.0057

10.013

21

10.017

32.3200

0.5399

110.296

31.3490

0.0848

0.1492

2000110

0.0115

10.003

21

0.0012

0.0095

0.0456

0.0558

10.7781

0.0437

0.0330

110.054

62.9060

10.659

21

0.0178

2.3880

0.1021

0.1713

1970175

0.0054

10.006

61

0.1382

0.0006

0.0742

0.0742

11.3380

0.0913

0.0851

110.032

60.6197

10.755

41

0.8765

0.0714

0.0684

0.1437

1975180

0.0079

0.0088

10.0363

0.0019

0.0624

0.0691

11.1510

0.1048

10.054

91

0.0319

1.0780

1.0770

10.2673

0.2621

0.0945

0.1750

1980185

0.0217

10.007

11

0.0284

0.0134

0.0495

0.0805

10.8095

0.0271

10.059

31

10.148

53.7240

10.749

91

0.2973

2.2990

0.0925

0.1847

1985190

0.0196

10.007

61

10.004

80.0139

0.0502

0.0672

10.6511

0.0119

0.0284

110.093

13.3030

10.961

51

10.062

82.3590

0.0712

0.1668

1990195

0.0123

0.0018

110.040

20.0083

0.0402

0.0478

10.5349

10.008

510.005

51

0.0047

2.5930

0.3183

110.637

11.7680

0.0777

0.1369

1995100

0.0105

0.0013

10.0135

0.0062

0.0549

0.0605

10.7295

0.0287

0.0011

110.039

51.6150

0.1785

10.1570

0.9567

0.1005

0.1623

2000105

0.0124

10.010

11

0.1006

0.0101

0.0371

0.0519

10.6943

0.0139

10.297

71

10.044

32.8320

11.653

01

1.2290

2.3140

0.0821

0.1521

2005110

0.0100

0.0035

110.086

80.0081

0.0510

0.0549

10.8017

0.0680

0.2887

110.053

51.6650

0.5417

110.919

01.3440

0.1167

0.1907

193512010

0.0108

0.0016

110.014

60.0077

0.0558

0.0600

10.8583

0.0298

0.0188

110.067

65.8210

0.8054

110.514

54.1420

0.0898

0.1751

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!D:

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

193516/68

0.0101

0.0090

10.001

610.073

60.0088

0.0958

0.1609

0.0690

0.8374

0.0087

10.052

310.000

210.087

72.1020

1.1200

10.461

111.760

01.8300

0.0892

0.1993

1935145

0.0113

0.0057

0.0023

10.042

60.0111

0.1173

0.1658

0.0589

0.5858

0.0110

10.060

510.000

210.038

51.0990

0.3932

0.4531

10.832

11.0850

0.0791

0.1935

1946155

0.0079

0.0088

10.000

410.095

40.0070

0.0692

0.1218

0.0490

0.8268

0.0117

10.095

810.000

210.063

01.2500

0.7953

10.100

111.263

01.1010

0.1268

0.2278

195616/68

0.0107

0.0120

10.005

910.083

30.0081

0.0937

0.1834

0.0884

1.0180

0.0586

10.033

510.000

310.148

51.4010

0.8016

10.821

011.002

01.0610

0.0679

0.1757

1935140

0.0109

0.0038

0.0012

10.024

70.0108

0.1405

0.1950

0.0657

0.6137

10.019

510.074

110.000

310.029

00.6541

0.1628

0.1591

10.339

00.6494

0.0719

0.1842

1941145

0.0117

0.0080

0.0036

10.063

80.0115

0.0832

0.1242

0.0500

0.5554

10.088

810.031

410.000

110.050

61.0890

0.4974

0.5601

10.889

41.0690

0.0877

0.2051

1946150

0.0008

0.0089

10.000

510.038

60.0001

0.0672

0.0992

0.0355

0.7604

10.005

60.0122

0.0001

10.021

60.0891

0.6939

10.108

210.393

60.0124

0.1649

0.2368

1951155

0.0150

0.0088

10.000

410.152

10.0138

0.0711

0.1417

0.0599

0.8911

0.0291

10.153

610.000

510.113

91.6370

0.4810

10.051

711.322

01.5040

0.0888

0.2137

1956160

0.0064

0.0304

10.017

710.128

00.0043

0.0609

0.1450

0.0699

1.2800

10.224

310.162

110.000

410.224

60.8148

1.6210

11.965

010.774

30.5470

0.0461

0.1537

196116/68

0.0136

10.000

20.0019

10.053

50.0107

0.1106

0.2049

0.0984

0.8031

0.1019

10.007

910.000

410.096

51.1670

10.010

80.1876

10.632

10.9153

0.0825

0.1884

7/196812010

0.0067

0.0056

10.004

20.0489

0.0022

0.1061

0.1940

0.0917

0.9209

0.1287

0.1039

0.0006

10.010

61.4340

0.6473

11.042

01.2000

0.4686

0.1002

0.1917

1970180

10.000

90.0064

10.004

00.1455

10.006

30.1637

0.2623

0.1101

1.2040

0.1895

0.1765

0.0022

0.0043

10.061

10.2805

10.420

91.3880

10.444

10.1038

0.1911

1980190

0.0107

0.0066

10.008

40.0694

0.0037

0.0998

0.2058

0.1006

0.7939

0.0718

0.1180

0.0011

10.045

41.2330

0.3681

10.960

01.0050

0.4231

0.0920

0.2014

1990100

0.0151

10.010

00.0074

10.032

90.0110

0.0719

0.1687

0.1001

0.6770

10.001

010.066

010.000

810.002

72.4050

10.682

40.8461

10.558

11.7550

0.0865

0.1755

2000110

0.0049

0.0176

10.012

20.0099

0.0028

0.0498

0.1127

0.0522

0.8228

0.0198

0.0409

0.0002

10.025

21.1310

1.7930

12.697

00.1380

0.6547

0.1125

0.1916

1970175

0.0097

10.010

20.0024

0.0838

0.0049

0.1821

0.2893

0.1230

1.3540

0.2473

0.2526

0.0037

10.070

00.4526

10.299

70.1685

0.5249

0.2291

0.0999

0.1794

1975180

10.002

50.0254

10.007

30.0618

10.008

50.1456

0.2348

0.0968

1.1580

0.0335

10.007

70.0000

0.1010

10.147

00.9195

10.643

30.4529

10.497

30.1042

0.1962

1980185

0.0093

0.0121

10.011

20.1035

0.0010

0.1104

0.2048

0.0929

0.8707

10.017

90.0445

0.0005

10.054

00.7147

0.5021

11.023

01.0090

0.0751

0.1094

0.2088

1985190

0.0133

0.0049

10.007

50.0245

0.0077

0.0924

0.2087

0.1090

0.7100

0.1696

0.1734

0.0014

10.053

81.2220

0.1977

10.580

30.2922

0.7041

0.0789

0.1882

1990195

0.0166

10.008

30.0065

10.059

80.0127

0.0775

0.1791

0.1091

0.5989

10.124

610.165

210.001

90.0255

1.8200

10.395

20.5065

10.847

81.3890

0.0811

0.1616

1995100

0.0161

10.012

00.0074

0.0008

0.0118

0.0652

0.1521

0.0848

0.7209

0.1601

0.0369

0.0002

10.034

42.0900

10.671

60.7383

0.0096

1.5330

0.1022

0.1889

2000105

0.0014

0.0297

10.022

60.0813

10.000

90.0430

0.1105

0.0621

0.7358

10.011

60.0113

0.0004

10.033

50.2775

2.2800

13.090

00.9378

10.168

10.0886

0.1673

2005110

0.0080

0.0066

10.001

610.072

60.0061

0.0536

0.1083

0.0318

0.8559

0.0368

0.0277

0.0000

10.006

01.2710

0.5151

10.430

610.719

50.9664

0.1297

0.2136

193512010

0.0082

0.0071

10.003

110.005

00.0051

0.1017

0.1801

0.0825

0.8867

0.0819

0.0493

0.0002

10.046

92.4340

1.1850

11.123

010.170

51.5100

0.0954

0.1951

TABLE!3d

:!Value



ortfolios!B

uilt!Usin

g!Equal1W

eighted!Securities

SUMMAR

Y!RE

SULTS!FO

R!TH

E!RE

GRESSION!(con

t.)

Statistics

¯ �0

¯ � 1¯ �2

¯ � 3�0�

Rf

s(�0)

s(�

1)

s(�2)

s(�3)

⇢ 0(�

0�R

f)⇢

M(�

1)

⇢0(�

2)

⇢0(�3)

t(¯ �0)

t(¯ �1)

t(¯ �2)

t(¯ �3)

t(�0�

Rf)

r2s(

r2)

Rp

=�0t+

�1t�

p+�2t�

2 p+

�3ts p

(ei)

+⌘

p

46

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Perio

d!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!A:

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

193516/68

0.0096

0.0043

11

0.0083

0.0451

0.0545

11

0.0080

0.0187

11

4.2460

1.5860

11

3.6620

0.2589

0.2666

1935145

0.0103

0.0088

11

0.0101

0.0610

0.0737

11

0.0103

10.044

81

11.9250

1.3600

11

1.8990

0.2677

0.2522

1946155

0.0093

0.0024

11

0.0083

0.0344

0.0432

11

10.050

50.0653

11

2.9550

0.6019

11

2.6530

0.2654

0.2938

195616/68

0.0092

0.0020

11

0.0066

0.0356

0.0416

11

0.2036

0.1328

11

3.1590

0.5888

11

2.2520

0.2461

0.2572

1935140

0.0098

0.0031

11

0.0097

0.0751

0.0877

11

10.057

010.106

61

11.0940

0.2986

11

1.0850

0.2276

0.2504

1941145

0.0109

0.0154

11

0.0107

0.0389

0.0524

11

0.1401

0.1098

11

2.1680

2.2810

11

2.1260

0.3152

0.2480

1946150

0.0059

0.0024

11

0.0052

0.0389

0.0475

11

0.0563

0.0703

11

1.1660

0.3969

11

1.0330

0.3477

0.3030

1951155

0.0127

0.0023

11

0.0115

0.0291

0.0387

11

10.201

80.0543

11

3.3760

0.4617

11

3.0460

0.1831

0.2616

1956160

0.0158

10.007

51

10.0137

0.0283

0.0316

11

0.0481

0.0255

11

4.3280

11.832

01

13.7380

0.1831

0.2646

196116/68

0.0048

0.0083

11

0.0018

0.0393

0.0461

11

0.2178

0.1292

11

1.1500

1.7110

11

0.4394

0.2881

0.2447

7/196812010

0.0092

0.0022

11

0.0047

0.0378

0.0544

11

0.0465

0.1277

11

5.5070

0.9199

11

2.8060

0.2830

0.2581

1970180

0.0069

0.0052

11

0.0014

0.0451

0.0648

11

0.0218

0.1182

11

1.7450

0.9262

11

0.3553

0.2972

0.2660

1980190

0.0155

10.002

51

10.0085

0.0401

0.0563

11

0.0264

0.0502

11

4.4530

10.505

01

12.4340

0.2616

0.2593

1990100

0.0096

0.0017

11

0.0055

0.0346

0.0469

11

0.0348

0.2096

11

3.1920

0.4184

11

1.8460

0.2515

0.2374

2000110

0.0067

0.0034

11

0.0046

0.0310

0.0509

11

0.0659

0.1848

11

2.4690

0.7671

11

1.7090

0.3021

0.2628

1970175

0.0066

0.0002

11

0.0018

0.0510

0.0654

11

0.0562

0.0970

11

1.0990

0.0239

11

0.3004

0.3149

0.2661

1975180

0.0086

0.0140

11

0.0026

0.0394

0.0684

11

10.091

80.1436

11

1.8570

1.7360

11

0.5690

0.2734

0.2636

1980185

0.0190

10.002

41

10.0107

0.0398

0.0526

11

0.0772

0.0138

11

4.0550

10.382

41

12.2700

0.3060

0.2561

1985190

0.0135

10.002

31

10.0079

0.0387

0.0575

11

10.043

20.0853

11

2.9610

10.338

11

11.7290

0.2238

0.2602

1990195

0.0096

0.0017

11

0.0056

0.0319

0.0468

11

0.0258

0.2612

11

2.5510

0.3107

11

1.5020

0.2366

0.2303

1995100

0.0120

0.0013

11

0.0077

0.0368

0.0461

11

0.0707

0.1688

11

2.7660

0.2483

11

1.7860

0.2730

0.2561

2000105

0.0089

0.0033

11

0.0066

0.0327

0.0446

11

0.0156

0.0282

11

2.3010

0.6270

11

1.7200

0.2645

0.2517

2005110

0.0038

0.0039

11

0.0019

0.0272

0.0543

11

0.1308

0.2791

11

1.1990

0.6140

11

0.5936

0.3307

0.2694

193512010

0.0094

0.0031

11

0.0063

0.0411

0.0544

11

0.0392

0.0815

11

6.8720

1.7420

11

4.5890

0.2724

0.2620

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!B:

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

193516/68

10.001

90.0301

10.012

11

10.003

20.0671

0.1584

0.0700

110.003

410.033

810.000

21

10.553

23.8040

13.475

01

10.941

70.0930

0.1658

1935145

10.001

10.0359

10.013

01

10.001

20.0685

0.1841

0.0831

110.001

510.000

110.000

21

10.184

52.2290

11.785

01

10.208

60.0719

0.1509

1946155

10.002

00.0267

10.011

21

10.002

90.0681

0.1502

0.0659

110.106

410.086

410.000

51

10.316

91.9450

11.863

01

10.469

10.1353

0.1974

195616/68

10.002

40.0278

10.012

21

10.005

00.0656

0.1403

0.0604

10.1384

10.036

810.000

11

10.451

32.4250

12.468

01

10.935

80.0778

0.1442

1935140

10.008

30.0474

10.021

91

10.008

40.0751

0.2151

0.0956

10.1757

10.055

810.000

61

10.931

71.8580

11.926

01

10.940

60.0551

0.1401

1941145

0.0074

0.0222

10.002

41

0.0072

0.0592

0.1395

0.0644

10.0478

0.1358

0.0003

10.9696

1.2310

10.292

01

0.9411

0.0917

0.1616

1946150

10.000

40.0162

10.006

11

10.001

10.0519

0.1171

0.0460

10.0609

0.1826

0.0003

110.060

31.0700

11.030

01

10.159

50.1866

0.2029

1951155

10.003

50.0372

10.016

31

10.004

80.0815

0.1777

0.0812

110.177

910.208

610.001

41

10.335

91.6210

11.554

01

10.452

60.0839

0.1790

1956160

0.0025

0.0246

10.015

71

0.0004

0.0465

0.1095

0.0526

110.164

010.439

110.000

61

0.4103

1.7390

12.307

01

0.0586

0.0648

0.1448

196116/68

10.005

70.0299

10.009

81

10.008

60.0758

0.1581

0.0653

10.2105

0.0907

0.0003

110.709

61.7940

11.430

01

11.076

00.0864

0.1439

7/196812010

0.0052

0.0125

10.005

61

0.0007

0.0714

0.1753

0.0836

10.0633

0.0772

0.0002

11.6560

1.6040

11.503

01

0.2208

0.1091

0.1661

1970180

10.002

30.0249

10.009

31

10.007

70.1000

0.2267

0.1050

10.0361

0.0048

10.000

51

10.258

41.2630

11.022

01

10.887

20.1166

0.1684

1980190

0.0120

0.0074

10.005

91

0.0050

0.0842

0.2016

0.1000

10.0109

0.0888

0.0004

11.6380

0.4220

10.676

01

0.6763

0.1061

0.1651

1990100

0.0074

0.0094

10.005

21

0.0033

0.0523

0.1502

0.0812

10.2103

0.1457

0.0009

11.6310

0.7225

10.732

81

0.7337

0.0879

0.1532

2000110

0.0049

0.0083

10.002

51

0.0029

0.0359

0.1264

0.0553

10.0295

0.0160

10.000

21

1.5790

0.7587

10.512

31

0.9189

0.1228

0.1753

1970175

0.0021

0.0097

10.004

31

10.002

70.0904

0.1921

0.0939

110.005

310.067

210.001

11

0.1972

0.4271

10.390

61

10.252

50.1105

0.1712

1975180

10.001

90.0363

10.010

51

10.007

90.1181

0.2661

0.1263

10.0524

0.0302

10.000

11

10.138

71.1580

10.703

91

10.572

10.1228

0.1679

1980185

0.0128

0.0102

10.005

71

0.0045

0.0870

0.1980

0.0944

110.145

110.024

610.000

51

1.2480

0.4366

10.508

21

0.4369

0.1102

0.1525

1985190

0.0124

0.0053

10.006

11

0.0067

0.0795

0.1987

0.1014

10.1534

0.1644

0.0011

11.3190

0.2249

10.511

91

0.7173

0.1067

0.1794

1990195

0.0038

0.0203

10.011

51

10.000

20.0585

0.1739

0.0939

10.2618

0.1881

0.0019

10.5451

0.9911

11.042

01

10.032

00.0629

0.1377

1995100

0.0146

10.005

40.0032

10.0103

0.0429

0.1107

0.0589

10.0907

10.010

610.000

21

2.8900

10.415

00.4585

12.0510

0.1161

0.1663

2000105

0.0055

0.0127

10.004

61

0.0032

0.0358

0.1132

0.0583

10.0768

10.010

910.000

21

1.3020

0.9547

10.666

71

0.7718

0.1054

0.1651

2005110

0.0039

0.0042

10.000

41

0.0019

0.0345

0.1320

0.0488

110.017

50.0165

10.000

11

0.9478

0.2701

10.072

41

0.4685

0.1377

0.1812

193512010

0.0021

0.0202

10.008

51

10.001

00.0696

0.1682

0.0779

10.0648

0.0365

0.0000

10.9171

3.6270

13.276

01

10.434

60.1020

0.1661

TABLE!3f:!Equ

al1W


ortfolio!!!!!!!!!+!!!!!!!5x5!Do

uble1Sort!T

est!P

ortfolios!B

uilt!Usin

g!Va

lue1Weighted!Securities

SUMMAR

Y!RE

SULTS!FO

R!TH

E!RE

GRESSION

Statistics

¯ �0

¯ � 1¯ �2

¯ � 3�0�

Rf

s(�0)

s(�

1)

s(�2)

s(�3)

⇢ 0(�

0�R

f)⇢

M(�

1)

⇢0(�

2)

⇢0(�3)

t(¯ �0)

t(¯ �1)

t(¯ �2)

t(¯ �3)

t(�0�

Rf)

r2s(

r2)

Rp

=�0t+

�1t�

p+�2t�

2 p+

�3ts p

(ei)

+⌘

p

47

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Perio

d!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!C:

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

193516/68

0.0089

0.0046

10.0105

0.0076

0.0472

0.0647

10.6843

0.0074

0.0363

110.018

73.7690

1.4090

10.3058

3.2110

0.1036

0.1715

1935145

0.0088

0.0087

10.0223

0.0086

0.0625

0.0834

10.5319

0.0087

10.005

61

10.036

01.6110

1.1880

10.4795

1.5860

0.0865

0.1567

1946155

0.0108

0.0058

110.073

90.0099

0.0380

0.0558

10.6840

10.164

70.0610

110.057

03.1230

1.1300

111.184

02.8490

0.1360

0.2024

195616/68

0.0074

0.0000

10.0676

0.0048

0.0376

0.0514

10.7920

0.1632

0.0846

10.0280

2.4100

0.0002

11.0460

1.5540

0.0926

0.1535

1935140

0.0080

0.0050

10.0132

0.0079

0.0760

0.0954

10.5202

10.065

80.0048

110.024

40.8877

0.4431

10.2143

0.8792

0.0749

0.1497

1941145

0.0097

0.0130

10.0330

0.0095

0.0416

0.0671

10.5496

10.031

710.049

01

10.049

71.8080

1.4980

10.4651

1.7690

0.1003

0.1647

1946150

0.0068

0.0045

110.042

10.0062

0.0404

0.0631

10.6603

10.020

10.0924

110.026

91.3120

0.5566

110.494

31.1840

0.1848

0.2027

1951155

0.0148

0.0070

110.105

70.0136

0.0353

0.0480

10.7111

10.333

40.0008

110.084

43.2520

1.1280

111.152

02.9770

0.0873

0.1916

1956160

0.0125

10.010

71

0.1178

0.0104

0.0333

0.0386

10.7273

0.0099

0.1083

10.0397

2.9030

12.144

01

1.2550

2.4110

0.0680

0.1417

196116/68

0.0040

0.0071

10.0341

0.0011

0.0400

0.0576

10.8346

0.1934

0.0361

10.0109

0.9502

1.1730

10.3881

0.2521

0.1089

0.1595

7/196812010

0.0093

0.0024

110.007

50.0048

0.0447

0.0671

10.8981

0.0026

0.0219

110.017

94.7110

0.8086

110.188

72.4320

0.1128

0.1661

1970180

0.0069

0.0050

110.007

50.0014

0.0541

0.0687

11.0780

10.040

610.008

51

0.0347

1.4640

0.8350

110.080

40.3046

0.1228

0.1675

1980190

0.0179

0.0025

110.087

20.0108

0.0462

0.0801

10.9636

0.0626

10.025

01

10.059

24.4520

0.3584

111.040

02.7040

0.0937

0.1655

1990100

0.0090

0.0007

10.0171

0.0049

0.0416

0.0553

10.7208

0.0175

0.0675

110.003

62.4760

0.1521

10.2722

1.3560

0.1089

0.1538

2000110

0.0050

10.000

61

0.0724

0.0030

0.0398

0.0650

10.8666

0.0390

0.0971

110.024

61.4500

10.102

31

0.9601

0.8572

0.1337

0.1769

1970175

0.0117

0.0126

110.218

90.0069

0.0612

0.0729

11.2070

10.132

210.038

41

10.037

41.6140

1.4630

111.540

00.9504

0.1202

0.1710

1975180

0.0043

0.0019

10.1892

10.001

70.0495

0.0670

10.9062

0.0072

10.023

41

0.0955

0.7451

0.2386

11.7720

10.287

10.1215

0.1584

1980185

0.0194

10.001

81

10.010

70.0111

0.0436

0.0698

10.7641

0.1478

10.074

31

10.058

63.7780

10.215

41

10.118

32.1640

0.0968

0.1631

1985190

0.0176

0.0062

110.151

20.0119

0.0464

0.0855

11.0870

10.004

00.0020

110.070

03.2130

0.6157

111.181

02.1880

0.0867

0.1693

1990195

0.0100

0.0016

110.007

50.0060

0.0380

0.0542

10.6810

10.063

70.1573

10.0153

2.2250

0.2458

110.092

91.3500

0.0919

0.1469

1995100

0.0098

10.001

51

0.0583

0.0056

0.0442

0.0540

10.7308

0.0992

10.026

31

10.022

01.8880

10.230

01

0.6769

1.0710

0.1282

0.1614

2000105

0.0084

0.0016

10.0277

0.0061

0.0419

0.0493

10.8496

0.0180

0.0286

10.0746

1.6960

0.2733

10.2770

1.2420

0.1264

0.1770

2005110

0.0009

10.002

41

0.1197

10.001

00.0355

0.0739

10.8561

0.0440

0.1279

110.126

40.2157

10.280

81

1.1860

10.250

00.1406

0.1838

193512010

0.0091

0.0033

10.0004

0.0060

0.0458

0.0660

10.8106

10.006

90.0280

110.019

46.0190

1.5310

10.0148

3.9730

0.1088

0.1685

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!D:

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

193516/68

10.002

50.0273

10.012

00.0408

10.003

80.0745

0.1549

0.0738

0.7096

10.003

910.003

30.0000

10.007

510.666

43.5300

13.253

01.1530

11.016

00.1144

0.1849

1935145

10.005

50.0375

10.016

40.0644

10.005

70.0864

0.1854

0.0966

0.6297

10.006

20.0319

0.0002

10.021

410.730

72.3150

11.939

01.1700

10.749

90.0974

0.1693

1946155

0.0032

0.0210

10.007

610.055

70.0023

0.0650

0.1385

0.0596

0.6567

10.159

410.072

310.000

310.043

70.5417

1.6600

11.392

010.929

10.3825

0.1575

0.2138

195616/68

10.004

40.0235

10.011

70.0975

10.007

00.0707

0.1378

0.0601

0.8064

0.1454

10.009

20.0000

0.0332

10.760

22.0850

12.385

01.4810

11.209

00.0948

0.1678

1935140

10.012

50.0483

10.024

80.0599

10.012

60.0886

0.2130

0.1059

0.5775

0.1656

10.025

210.000

410.026

411.190

01.9100

11.973

00.8740

11.197

00.0832

0.1617

1941145

0.0028

0.0248

10.006

40.0697

0.0026

0.0836

0.1469

0.0842

0.6913

0.0251

0.1585

0.0009

10.015

00.2571

1.3050

10.589

30.7807

0.2366

0.1143

0.1778

1946150

0.0042

0.0117

10.003

610.047

00.0035

0.0516

0.1139

0.0442

0.6354

10.019

50.1369

0.0003

10.034

60.6266

0.7985

10.635

010.572

50.5268

0.2176

0.2158

1951155

0.0023

0.0302

10.011

510.064

40.0010

0.0765

0.1598

0.0720

0.6826

10.224

210.186

210.001

010.061

20.2280

1.4660

11.241

010.731

20.1040

0.0975

0.1956

1956160

10.000

30.0164

10.013

90.1558

10.002

40.0509

0.1039

0.0513

0.7042

10.264

410.448

010.000

80.0142

10.046

21.2220

12.099

01.7140

10.366

00.0799

0.1604

196116/68

10.007

10.0282

10.010

20.0587

10.010

10.0814

0.1568

0.0656

0.8695

0.2492

0.1163

0.0006

0.0393

10.828

31.7050

11.481

00.6402

11.169

00.1047

0.1727

7/196812010

0.0045

0.0138

10.006

40.0030

10.000

10.0819

0.1795

0.0885

0.9553

0.0793

0.0535

0.0005

0.0087

1.2310

1.7300

11.626

00.0714

10.020

20.1325

0.1834

1970180

10.003

70.0283

10.011

010.006

910.009

20.1122

0.2315

0.1110

1.1640

0.0618

10.028

410.000

30.0810

10.380

41.4050

11.135

010.068

210.941

20.1390

0.1833

1980190

0.0141

0.0086

10.004

710.054

10.0071

0.1000

0.2033

0.1092

1.0620

0.0719

0.0986

0.0011

10.040

91.6220

0.4845

10.492

410.585

50.8138

0.1206

0.1802

1990100

0.0057

0.0106

10.006

40.0242

0.0017

0.0630

0.1550

0.0833

0.7836

0.1987

0.1422

0.0012

0.0207

1.0470

0.7849

10.885

80.3547

0.3023

0.1298

0.1793

2000110

0.0027

0.0064

10.003

50.0717

0.0006

0.0405

0.1360

0.0531

0.8316

0.0803

10.046

710.000

210.005

50.7523

0.5397

10.755

70.9899

0.1659

0.1540

0.1949

1970175

0.0068

0.0226

10.004

610.211

30.0020

0.1038

0.2193

0.1050

1.3360

10.021

410.094

210.000

90.0363

0.5520

0.8751

10.374

011.342

00.1604

0.1292

0.1844

1975180

10.008

70.0342

10.014

30.1515

10.014

70.1264

0.2663

0.1302

0.9575

0.0987

10.024

810.000

10.0188

10.584

71.0890

10.930

11.3420

10.991

20.1525

0.1802

1980185

0.0123

0.0119

10.006

70.0013

0.0040

0.0964

0.2006

0.0978

0.8104

10.060

710.007

010.000

310.056

21.0840

0.5019

10.577

20.0139

0.3527

0.1183

0.1721

1985190

0.0159

0.0071

10.004

010.093

00.0102

0.1024

0.2004

0.1164

1.2300

0.1507

0.1706

0.0020

10.049

31.3160

0.3022

10.289

510.641

40.8491

0.1258

0.1906

1990195

0.0027

0.0222

10.012

80.0067

10.001

30.0669

0.1747

0.0958

0.7096

0.2440

0.1912

0.0022

0.0376

0.3380

1.0780

11.131

00.0802

10.166

90.1036

0.1708

1995100

0.0110

10.003

70.0008

0.0594

0.0067

0.0579

0.1221

0.0621

0.8294

0.1435

0.0058

10.000

10.0143

1.6090

10.257

00.1064

0.6081

0.9857

0.1550

0.1888

2000105

0.0040

0.0135

10.006

00.0341

0.0017

0.0420

0.1183

0.0541

0.8265

0.0922

10.047

710.000

30.0863

0.8011

0.9653

10.946

60.3504

0.3470

0.1458

0.1916

2005110

0.0011

10.001

110.000

60.1066

10.000

90.0380

0.1425

0.0487

0.8147

0.0396

10.055

410.000

210.103

90.2364

10.066

510.100

11.1100

10.197

20.1591

0.2022

193512010

0.0014

0.0197

10.008

80.0197

10.001

70.0788

0.1691

0.0824

0.8557

0.0753

0.0343

0.0003

0.0001

0.5391

3.5190

13.242

00.6938

10.655

20.1245

0.1842

TABLE!3f:!Equ

al1W


ortfolio!!!!!!!!!+!!!!!!!5x5!Do

uble1Sort!T

est!P

ortfolios!B

uilt!Usin

g!Va


SUMMAR

Y!RE

SULTS!FO

R!TH

E!RE

GRESSION!(con

t.)

Statistics

¯ �0

¯ � 1¯ �2

¯ � 3�0�

Rf

s(�0)

s(�

1)

s(�2)

s(�3)

⇢ 0(�

0�R

f)⇢

M(�

1)

⇢0(�

2)

⇢0(�3)

t(¯ �0)

t(¯ �1)

t(¯ �2)

t(¯ �3)

t(�0�

Rf)

r2s(

r2)

Rp

=�0t+

�1t�

p+�2t�

2 p+

�3ts p

(ei)

+⌘

p

48

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Perio

d!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!A:

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

193516/68

0.0053

0.0071

11

0.0040

0.0371

0.0545

11

0.0037

0.0385

11

2.8610

2.6130

11

2.1530

0.2589

0.2666

1935145

0.0029

0.0123

11

0.0027

0.0482

0.0730

11

0.0027

10.044

71

10.6796

1.9300

11

0.6457

0.2677

0.2522

1946155

0.0080

0.0028

11

0.0070

0.0260

0.0368

11

0.0767

0.0727

11

3.3650

0.8473

11

2.9680

0.2654

0.2938

195616/68

0.0053

0.0060

11

0.0027

0.0334

0.0470

11

0.2914

0.1807

11

1.9360

1.5620

11

0.9749

0.2461

0.2572

1935140

0.0017

0.0085

11

0.0017

0.0571

0.0873

11

10.010

610.109

61

10.2566

0.8214

11

0.2452

0.2276

0.2504

1941145

0.0042

0.0168

11

0.0040

0.0353

0.0518

11

0.1891

0.1567

11

0.9199

2.5150

11

0.8721

0.3152

0.2480

1946150

0.0046

0.0027

11

0.0039

0.0312

0.0416

11

0.1523

0.0352

11

1.1400

0.4984

11

0.9740

0.3477

0.3030

1951155

0.0114

0.0030

11

0.0101

0.0191

0.0316

11

10.065

50.0893

11

4.6160

0.7384

11

4.1130

0.1831

0.2616

1956160

0.0146

10.006

11

10.0125

0.0190

0.0372

11

0.3003

0.1473

11

5.9630

11.263

01

15.0840

0.1831

0.2646

196116/68

10.000

90.0140

11

10.003

90.0392

0.0511

11

0.2260

0.1437

11

10.229

02.6030

11

10.938

30.2881

0.2447

7/196812010

0.0077

0.0034

11

0.0031

0.0395

0.0591

11

0.1250

0.1968

11

4.3780

1.3050

11

1.7960

0.2830

0.2581

1970180

0.0005

0.0100

11

10.004

90.0472

0.0667

11

0.2074

0.2249

11

0.1312

1.7260

11

11.201

00.2972

0.2660

1980190

0.0183

10.004

81

10.0112

0.0434

0.0622

11

0.0711

0.2373

11

4.8320

10.895

01

12.9850

0.2616

0.2593

1990100

0.0084

0.0030

11

0.0043

0.0386

0.0578

11

0.1047

0.1857

11

2.4910

0.5882

11

1.2830

0.2515

0.2374

2000110

0.0069

0.0027

11

0.0048

0.0299

0.0542

11

0.0607

0.1263

11

2.6400

0.5685

11

1.8540

0.3021

0.2628

1970175

0.0065

10.000

81

10.0017

0.0490

0.0633

11

0.1329

0.2010

11

1.1310

10.113

01

10.3006

0.3149

0.2661

1975180

10.003

30.0234

11

10.009

30.0464

0.0691

11

0.2684

0.2614

11

10.598

72.8700

11

11.714

00.2734

0.2636

1980185

0.0179

10.000

51

10.0096

0.0423

0.0580

11

0.1673

0.2079

11

3.5900

10.072

71

11.9400

0.3060

0.2561

1985190

0.0202

10.008

91

10.0146

0.0434

0.0634

11

10.015

60.2491

11

3.9500

11.195

01

12.8620

0.2238

0.2602

1990195

0.0084

0.0027

11

0.0044

0.0381

0.0551

11

0.1881

0.2861

11

1.8670

0.4138

11

0.9889

0.2366

0.2303

1995100

0.0108

0.0026

11

0.0065

0.0388

0.0585

11

0.0449

0.0906

11

2.3620

0.3781

11

1.4340

0.2730

0.2561

2000105

0.0094

0.0018

11

0.0071

0.0299

0.0544

11

10.077

210.008

41

12.6650

0.2794

11

2.0390

0.2645

0.2517

2005110

0.0036

0.0039

11

0.0016

0.0280

0.0507

11

0.2149

0.2612

11

1.0880

0.6466

11

0.4996

0.3307

0.2694

193512010

0.0066

0.0050

11

0.0035

0.0385

0.0572

11

0.1263

0.1364

11

5.1950

2.6640

11

2.7610

0.2724

0.2620

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!B:

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

193516/68

0.0060

0.0059

0.0003

10.0047

0.0657

0.1213

0.0497

10.0043

10.009

60.0001

11.8410

0.9705

0.1207

11.4430

0.2777

0.2691

1935145

0.0111

10.002

20.0053

10.0109

0.0818

0.1391

0.0538

10.0111

10.101

410.000

11

1.5500

10.184

81.1270

11.5300

0.2675

0.2691

1946155

10.000

60.0177

10.005

71

10.001

50.0501

0.1046

0.0371

10.0071

10.039

710.000

11

10.123

11.8490

11.689

01

10.329

60.3199

0.2918

195616/68

0.0069

0.0036

0.0008

10.0043

0.0606

0.1171

0.0545

10.1630

0.1162

0.0003

11.3980

0.3721

0.1691

10.8708

0.2527

0.2472

1935140

0.0116

10.009

50.0067

10.0116

0.0990

0.1723

0.0635

10.0463

10.085

010.000

21

0.9901

10.463

60.8859

10.9835

0.2201

0.2680

1941145

0.0104

0.0063

0.0037

10.0102

0.0558

0.0853

0.0399

10.1600

10.194

00.0001

11.4460

0.5734

0.7132

11.4170

0.3237

0.2616

1946150

0.0001

0.0096

10.002

41

10.000

60.0530

0.1008

0.0299

10.0298

10.015

310.000

11

0.0158

0.7400

10.625

61

10.081

20.4011

0.2972

1951155

10.001

20.0257

10.009

01

10.002

50.0474

0.1085

0.0431

110.054

910.094

010.000

11

10.201

61.8330

11.621

01

10.401

90.2387

0.2646

1956160

0.0111

0.0025

10.004

21

0.0089

0.0407

0.0987

0.0482

10.3218

0.2000

0.0006

12.1030

0.1936

10.676

11

1.6990

0.2051

0.2375

196116/68

0.0042

0.0043

0.0041

10.0012

0.0709

0.1284

0.0583

10.1210

0.0842

0.0001

10.5563

0.3165

0.6599

10.1634

0.2845

0.2498

7/196812010

0.0056

0.0087

10.002

61

0.0011

0.0727

0.1495

0.0683

10.0657

10.028

510.000

31

1.7430

1.3160

10.862

21

0.3344

0.3050

0.2536

1970180

0.0022

0.0073

0.0011

110.003

30.1086

0.1947

0.0744

10.0805

10.015

610.000

41

0.2290

0.4327

0.1732

110.349

10.3377

0.2589

1980190

0.0084

0.0194

10.012

31

0.0014

0.0926

0.1792

0.0673

10.0381

0.0127

10.000

31

1.0430

1.2410

12.098

01

0.1695

0.3150

0.2577

1990100

0.0071

0.0053

10.000

81

0.0031

0.0548

0.1478

0.0870

10.0119

10.070

610.000

11

1.4990

0.4104

10.105

51

0.6425

0.2549

0.2219

2000110

0.0063

0.0045

10.000

91

0.0043

0.0362

0.1115

0.0613

10.1579

10.032

310.000

41

2.0120

0.4617

10.166

71

1.3560

0.3126

0.2652

1970175

10.001

50.0141

10.006

11

10.006

30.0979

0.1749

0.0716

10.0782

10.084

010.000

51

10.131

50.6829

10.717

91

10.546

70.3428

0.2549

1975180

0.0085

0.0027

0.0082

10.0025

0.1210

0.2157

0.0817

10.0638

0.0017

10.000

51

0.5968

0.1045

0.8510

10.1760

0.3274

0.2638

1980185

0.0157

0.0042

10.002

01

0.0074

0.1056

0.1907

0.0689

10.0732

0.0667

10.000

31

1.2620

0.1850

10.242

31

0.5979

0.3655

0.2525

1985190

0.0038

0.0319

10.021

11

10.001

80.0720

0.1556

0.0603

110.075

510.108

910.000

31

0.4522

1.7410

12.969

01

10.213

40.2696

0.2549

1990195

0.0082

0.0016

0.0013

10.0042

0.0597

0.1573

0.0931

110.000

310.127

910.000

41

1.1690

0.0850

0.1159

10.6028

0.2164

0.1985

1995100

0.0072

0.0121

10.004

71

0.0029

0.0468

0.1271

0.0735

10.0208

0.0163

0.0004

11.3010

0.8054

10.548

31

0.5269

0.2961

0.2313

2000105

0.0088

0.0038

10.001

11

0.0066

0.0377

0.1193

0.0774

10.1165

10.113

110.000

91

1.9910

0.2709

10.122

31

1.4900

0.2865

0.2467

2005110

0.0028

0.0062

10.001

01

0.0008

0.0332

0.0953

0.0313

10.1908

0.0839

0.0001

10.7021

0.5557

10.275

51

0.2054

0.3264

0.2811

193512010

0.0058

0.0075

10.001

31

0.0027

0.0696

0.1377

0.0608

10.0767

10.021

710.000

11

2.5130

1.6360

10.659

01

1.1640

0.2930

0.2607

TABLE!3g:!V

alue


ortfolio!!!!!!!!!+!!!!!!!5x5!Do

uble1Sort!T

est!P

ortfolios!B

uilt!Usin

g!Eq

ual1W

eighted!Securities

SUMMAR

Y!RE

SULTS!FO

R!TH

E!RE

GRESSION

Statistics

¯ �0

¯ � 1¯ �2

¯ � 3�0�

Rf

s(�0)

s(�

1)

s(�2)

s(�3)

⇢ 0(�

0�R

f)⇢

M(�

1)

⇢0(�

2)

⇢0(�3)

t(¯ �0)

t(¯ �1)

t(¯ �2)

t(¯ �3)

t(�0�

Rf)

r2s(

r2)

Rp

=�0t+

�1t�

p+�2t�

2 p+

�3ts p

(ei)

+⌘

p

49

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Perio

d!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!C:

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

193516/68

0.0047

0.0032

10.0574

0.0034

0.0386

0.0507

10.5088

0.0031

10.067

91

0.0357

2.4570

1.2440

12.2600

1.7780

0.3455

0.2734

1935145

0.0016

0.0026

10.1264

0.0015

0.0497

0.0656

10.4548

0.0014

10.174

31

0.0115

0.3704

0.4530

13.1800

0.3374

0.3396

0.2713

1946155

0.0085

0.0055

110.056

10.0075

0.0275

0.0417

10.3915

0.0631

10.019

71

10.013

83.3850

1.4340

111.569

03.0100

0.3579

0.2958

195616/68

0.0045

0.0018

10.0880

0.0019

0.0349

0.0421

10.6137

0.2784

0.1228

10.0957

1.5660

0.5238

11.7560

0.6474

0.3407

0.2577

1935140

0.0005

0.0006

10.0858

0.0005

0.0587

0.0801

10.4831

10.014

010.188

11

10.005

20.0764

0.0659

11.4960

0.0653

0.3204

0.2769

1941145

0.0029

0.0049

10.1744

0.0027

0.0369

0.0429

10.4177

0.1926

10.126

01

0.0334

0.6059

0.8894

13.2340

0.5598

0.3623

0.2651

1946150

0.0044

0.0037

110.015

00.0037

0.0305

0.0472

10.3236

0.1673

10.040

91

10.029

31.1110

0.5995

110.359

30.9412

0.4346

0.2956

1951155

0.0126

0.0073

110.097

10.0114

0.0237

0.0356

10.4483

10.097

710.068

81

0.0052

4.1240

1.5790

111.678

03.7200

0.2812

0.2777

1956160

0.0143

10.006

31

0.0099

0.0122

0.0240

0.0354

10.4679

0.1459

0.1398

10.0173

4.6220

11.381

01

0.1645

3.9390

0.2675

0.2572

196116/68

10.002

10.0072

10.1400

10.005

00.0394

0.0453

10.6917

0.2408

0.0830

10.1492

10.508

11.5080

11.9200

11.213

00.3895

0.2476

7/196812010

0.0076

0.0012

10.0261

0.0031

0.0425

0.0603

10.6659

0.0997

0.0108

10.0165

4.0530

0.4309

10.8851

1.6550

0.3497

0.2582

1970180

0.0020

0.0016

10.0849

10.003

40.0481

0.0686

10.8647

0.1637

10.084

81

0.0690

0.4809

0.2735

11.1280

10.825

20.3550

0.2672

1980190

0.0190

10.002

11

10.044

50.0119

0.0452

0.0686

10.6263

0.0395

0.0196

110.056

44.8250

10.354

51

10.816

03.0470

0.3218

0.2548

1990100

0.0089

0.0020

10.0068

0.0048

0.0445

0.0553

10.6216

0.1241

10.014

91

0.0280

2.2930

0.4192

10.1251

1.2440

0.3437

0.2517

2000110

0.0045

10.001

61

0.0828

0.0024

0.0363

0.0568

10.5668

0.0281

0.0930

10.0105

1.4130

10.317

01

1.6780

0.7627

0.3701

0.2517

1970175

0.0071

0.0048

110.097

10.0023

0.0509

0.0682

10.9935

0.1247

10.124

41

0.0570

1.1880

0.6012

110.829

40.3881

0.3714

0.2664

1975180

10.001

10.0031

10.2411

10.007

10.0460

0.0741

10.7035

0.1998

10.060

71

0.0641

10.210

20.3523

12.9080

11.333

00.3382

0.2685

1980185

0.0183

10.001

81

0.0132

0.0100

0.0426

0.0657

10.6204

0.1451

0.0065

110.044

43.6440

10.238

71

0.1808

2.0030

0.3647

0.2592

1985190

0.0211

10.002

61

10.094

10.0155

0.0464

0.0689

10.6016

10.031

50.0147

110.063

33.8580

10.323

71

11.327

02.8400

0.2809

0.2392

1990195

0.0076

10.001

71

0.0659

0.0036

0.0427

0.0494

10.6218

0.1909

10.006

21

0.0281

1.5040

10.300

11

0.8998

0.7172

0.2847

0.2392

1995100

0.0127

0.0060

110.064

30.0084

0.0454

0.0582

10.5778

0.0903

10.028

21

0.0284

2.3740

0.8802

110.943

71.5810

0.4071

0.2516

2000105

0.0056

10.004

91

0.1278

0.0033

0.0387

0.0526

10.5929

10.091

110.103

41

0.0130

1.2240

10.786

91

1.8280

0.7338

0.3697

0.2461

2005110

0.0022

0.0011

10.0553

0.0003

0.0313

0.0570

10.5315

0.2000

0.2507

10.0104

0.6050

0.1678

10.8824

0.0796

0.3708

0.2595

193512010

0.0064

0.0020

10.0399

0.0032

0.0409

0.0563

10.6017

0.1096

10.015

61

0.0248

4.6970

1.0900

12.0010

2.4070

0.3479

0.2649

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!D:

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

193516/68

10.002

20.0145

10.004

90.0777

10.003

50.0644

0.1110

0.0419

0.5296

10.003

90.0858

0.0002

0.0544

10.679

72.6110

12.355

02.9390

11.085

00.3592

0.2743

1935145

10.008

00.0174

10.006

00.1526

10.008

10.0734

0.1187

0.0409

0.4712

10.007

810.023

60.0001

0.0246

11.243

01.6800

11.672

03.7070

11.265

00.3506

0.2728

1946155

0.0029

0.0140

10.003

510.039

70.0019

0.0451

0.0922

0.0304

0.3765

0.1471

0.1096

0.0000

10.010

50.6999

1.6590

11.267

011.154

00.4700

0.3778

0.2902

195616/68

10.001

20.0123

10.005

10.1062

10.003

80.0691

0.1181

0.0500

0.6552

0.2760

0.1789

0.0004

0.1321

10.211

01.2730

11.255

01.9860

10.672

20.3517

0.2635

1935140

10.005

30.0100

10.003

80.1007

10.005

30.0882

0.1469

0.0471

0.5251

0.1681

0.0189

0.0001

0.0071

10.503

10.5715

10.682

31.6160

10.510

50.3217

0.2830

1941145

10.011

20.0263

10.008

50.2140

10.011

40.0511

0.0728

0.0323

0.3937

0.1296

10.250

80.0000

0.0466

11.693

02.7920

12.049

04.2110

11.728

00.3847

0.2584

1946150

10.000

20.0103

10.002

70.0009

10.000

90.0512

0.0929

0.0273

0.3416

0.1986

0.2164

0.0001

10.027

410.033

30.8553

10.766

70.0201

10.133

70.4620

0.2761

1951155

0.0060

0.0177

10.004

310.080

20.0048

0.0382

0.0923

0.0334

0.4073

10.053

310.057

410.000

10.0084

1.2140

1.4850

11.004

011.525

00.9657

0.2937

0.2814

1956160

0.0107

0.0011

10.003

90.0243

0.0086

0.0397

0.0947

0.0417

0.4570

10.039

00.0773

0.0001

0.0013

2.0880

0.0909

10.732

20.4119

1.6760

0.2777

0.2603

196116/68

10.009

10.0197

10.005

90.1609

10.012

10.0824

0.1314

0.0551

0.7567

0.3018

0.2073

0.0006

0.2207

11.049

01.4240

11.019

02.0170

11.387

00.4011

0.2552

7/196812010

0.0027

0.0118

10.005

90.0431

10.001

80.0865

0.1542

0.0682

0.7143

0.1781

0.0702

0.0003

0.0499

0.7080

1.7210

11.954

01.3610

10.477

10.3819

0.2626

1970180

10.005

90.0164

10.007

10.1014

10.011

30.1296

0.2063

0.0853

0.9497

0.2298

0.0876

0.0009

0.1749

10.520

40.9113

10.962

61.2270

11.005

00.3987

0.2712

1980190

0.0076

0.0214

10.013

40.0000

0.0006

0.1167

0.2031

0.0883

0.7457

0.1538

0.1013

0.0009

10.007

90.7517

1.2100

11.739

010.000

20.0581

0.3696

0.2643

1990100

0.0045

0.0119

10.005

80.0240

0.0004

0.0668

0.1332

0.0697

0.6597

0.1889

0.0949

0.0005

0.0384

0.7694

1.0290

10.963

60.4175

0.0664

0.3557

0.2589

2000110

0.0028

0.0031

10.002

50.0877

0.0007

0.0346

0.1087

0.0510

0.5342

0.1305

10.026

810.000

40.0028

0.9355

0.3279

10.573

81.8860

0.2491

0.4090

0.2566

1970175

0.0033

0.0114

10.003

510.081

410.001

50.1134

0.1703

0.0669

1.0350

0.2012

0.0056

0.0001

0.1789

0.2483

0.5681

10.441

710.667

210.110

30.3968

0.2665

1975180

10.009

60.0212

10.008

90.2422

10.015

60.1477

0.2373

0.1030

0.8717

0.2276

0.1124

0.0014

0.1553

10.549

90.7562

10.732

52.3580

10.896

10.3965

0.2759

1980185

0.0149

0.0047

10.002

70.0173

0.0065

0.1233

0.2066

0.0846

0.7035

0.2440

0.1507

0.0013

0.0398

1.0220

0.1918

10.269

50.2085

0.4526

0.4156

0.2630

1985190

0.0031

0.0351

10.022

510.012

710.002

50.1027

0.1862

0.0853

0.7483

0.0151

0.0075

0.0003

10.047

80.2570

1.6000

12.237

010.143

710.209

50.3237

0.2559

1990195

10.002

20.0207

10.013

10.1006

10.006

20.0792

0.1405

0.0768

0.7063

0.1869

0.1030

0.0007

0.0530

10.240

21.2480

11.451

01.2090

10.666

60.2924

0.2497

1995100

0.0134

0.0037

0.0016

10.062

90.0091

0.0484

0.1184

0.0566

0.5591

0.1390

0.0503

0.0001

0.0212

2.3470

0.2659

0.2395

10.954

71.5990

0.4227

0.2553

2000105

0.0033

0.0018

10.003

80.1341

0.0010

0.0337

0.1122

0.0625

0.5553

0.1417

10.140

310.000

80.0170

0.8290

0.1379

10.516

12.0490

0.2633

0.4012

0.2486

2005110

0.0006

0.0049

10.001

80.0608

10.001

30.0351

0.0977

0.0306

0.5125

0.0842

0.1163

0.0001

10.007

40.1530

0.4264

10.503

81.0060

10.314

40.4150

0.2609

193512010

0.0006

0.0130

10.005

50.0583

10.002

60.0776

0.1368

0.0581

0.6395

0.1882

0.0755

0.0003

0.0518

0.2165

2.8570

12.844

02.7520

10.997

10.3719

0.2679

TABLE!3g:!V

alue


ortfolio!!!!!!!!!+!!!!!!!5x5!Do

uble1Sort!T

est!P

ortfolios!B

uilt!Usin

g!Eq

ual1W

eighted!Securities

SUMMAR

Y!RE

SULTS!FO

R!TH

E!RE

GRESSION!(con

t.)

Statistics

¯ �0

¯ � 1¯ �2

¯ � 3�0�

Rf

s(�0)

s(�

1)

s(�2)

s(�3)

⇢ 0(�

0�R

f)⇢

M(�

1)

⇢0(�

2)

⇢0(�3)

t(¯ �0)

t(¯ �1)

t(¯ �2)

t(¯ �3)

t(�0�

Rf)

r2s(

r2)

Rp

=�0t+

�1t�

p+�2t�

2 p+

�3ts p

(ei)

+⌘

p

50

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Perio

d!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!A:

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

193516/68

0.0080

0.0044

11

0.0067

0.0489

0.0467

11

0.0065

0.0368

11

3.2830

1.8990

11

2.7460

0.2589

0.2666

1935145

0.0080

0.0077

11

0.0078

0.0667

0.0570

11

0.0080

10.005

01

11.3680

1.5460

11

1.3430

0.2677

0.2522

1946155

0.0091

0.0024

11

0.0082

0.0370

0.0395

11

10.043

30.0621

11

2.6990

0.6658

11

2.4200

0.2654

0.2938

195616/68

0.0072

0.0032

11

0.0046

0.0380

0.0420

11

0.2419

0.0754

11

2.3130

0.9322

11

1.4690

0.2461

0.2572

1935140

0.0071

0.0039

11

0.0070

0.0820

0.0654

11

10.101

410.095

01

10.7304

0.5080

11

0.7226

0.2276

0.2504

1941145

0.0090

0.0121

11

0.0088

0.0427

0.0451

11

0.0327

0.1966

11

1.6310

2.0850

11

1.5930

0.3152

0.2480

1946150

0.0028

0.0048

11

0.0021

0.0420

0.0429

11

0.0592

0.0532

11

0.5075

0.8716

11

0.3845

0.3477

0.3030

1951155

0.0155

0.0000

11

0.0143

0.0303

0.0360

11

10.272

90.0579

11

3.9550

10.005

61

13.6380

0.1831

0.2616

1956160

0.0107

10.002

41

10.0086

0.0268

0.0309

11

0.1467

0.0264

11

3.0950

10.598

11

12.4810

0.1831

0.2646

196116/68

0.0048

0.0069

11

0.0019

0.0439

0.0478

11

0.2477

0.0761

11

1.0420

1.3720

11

0.4066

0.2881

0.2447

7/196812010

0.0093

0.0019

11

0.0047

0.0412

0.0530

11

0.1089

0.1453

11

5.0760

0.7919

11

2.6050

0.2830

0.2581

1970180

0.0086

0.0030

11

0.0031

0.0509

0.0601

11

0.1061

0.1456

11

1.9410

0.5736

11

0.7104

0.2972

0.2660

1980190

0.0172

10.003

71

10.0101

0.0447

0.0564

11

0.0500

0.0989

11

4.4110

10.756

71

12.6120

0.2616

0.2593

1990100

0.0056

0.0056

11

0.0015

0.0366

0.0506

11

0.1070

0.1647

11

1.7470

1.2700

11

0.4678

0.2515

0.2374

2000110

0.0073

0.0019

11

0.0052

0.0294

0.0463

11

0.0914

0.1688

11

2.8380

0.4685

11

2.0390

0.3021

0.2628

1970175

0.0072

0.0001

11

0.0025

0.0569

0.0628

11

0.1635

0.1369

11

1.0800

0.0134

11

0.3656

0.3149

0.2661

1975180

0.0124

0.0079

11

0.0064

0.0445

0.0580

11

10.022

10.1481

11

2.3670

1.1510

11

1.2300

0.2734

0.2636

1980185

0.0212

10.004

11

10.0128

0.0448

0.0543

11

0.0399

0.0737

11

4.0050

10.645

91

12.4380

0.3060

0.2561

1985190

0.0155

10.003

81

10.0099

0.0429

0.0557

11

0.0452

0.1160

11

3.0620

10.581

01

11.9500

0.2238

0.2602

1990195

0.0037

0.0072

11

10.000

30.0357

0.0475

11

0.1036

0.1412

11

0.8816

1.2810

11

10.065

70.2366

0.2303

1995100

0.0106

0.0026

11

0.0063

0.0373

0.0518

11

0.1218

0.1804

11

2.4080

0.4309

11

1.4400

0.2730

0.2561

2000105

0.0103

0.0011

11

0.0080

0.0270

0.0422

11

0.1559

0.0388

11

3.2440

0.2232

11

2.5450

0.2645

0.2517

2005110

0.0039

0.0028

11

0.0019

0.0301

0.0476

11

0.0311

0.2561

11

1.0940

0.4910

11

0.5476

0.3307

0.2694

193512010

0.0087

0.0030

11

0.0056

0.0447

0.0503

11

0.0525

0.1051

11

5.8790

1.7940

11

3.7860

0.2724

0.2620

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!B:

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

193516/68

0.0016

0.0160

10.004

61

0.0003

0.0784

0.1498

0.0613

110.000

210.123

410.000

61

0.4172

2.1350

11.511

01

0.0840

0.0835

0.1559

1935145

10.002

00.0226

10.004

71

10.002

10.0885

0.1492

0.0498

110.002

310.206

810.000

51

10.253

41.7360

11.082

01

10.272

00.0718

0.1542

1946155

0.0052

0.0094

10.002

71

0.0042

0.0678

0.1306

0.0505

10.0101

0.0201

10.000

21

0.8334

0.7926

10.580

51

0.6811

0.1156

0.1751

195616/68

0.0020

0.0154

10.006

11

10.000

70.0774

0.1648

0.0767

110.005

310.140

010.001

11

0.3094

1.1440

10.976

91

10.103

20.0680

0.1373

1935140

10.002

40.0175

10.004

11

10.002

50.1055

0.1765

0.0550

110.050

910.217

510.000

71

10.193

20.8358

10.632

41

10.199

40.0499

0.1357

1941145

10.001

40.0287

10.005

41

10.001

60.0636

0.1096

0.0434

110.014

810.181

110.000

21

10.172

22.0270

10.964

11

10.199

30.0976

0.1711

1946150

0.0025

0.0052

10.000

11

0.0018

0.0663

0.1138

0.0352

10.0105

0.0765

0.0000

10.2903

0.3568

10.012

31

0.2124

0.1544

0.1831

1951155

0.0078

0.0137

10.005

31

0.0066

0.0696

0.1463

0.0624

10.0060

10.025

510.000

31

0.8704

0.7229

10.657

71

0.7352

0.0768

0.1590

1956160

0.0048

0.0136

10.008

71

0.0027

0.0547

0.1536

0.0800

110.284

910.401

810.001

91

0.6802

0.6856

10.842

91

0.3805

0.0419

0.0936

196116/68

0.0001

0.0166

10.004

41

10.002

90.0896

0.1727

0.0749

10.0639

0.0013

10.000

51

0.0060

0.9117

10.557

01

10.305

30.0854

0.1581

7/196812010

0.0061

0.0073

10.002

11

0.0016

0.0810

0.1732

0.0806

10.0418

0.0481

0.0004

11.7100

0.9562

10.580

01

0.4448

0.0880

0.1576

1970180

10.003

70.0262

10.009

71

10.009

20.1120

0.2073

0.0829

110.024

910.025

410.000

31

10.384

51.4500

11.345

01

10.944

60.0915

0.1625

1980190

0.0040

0.0260

10.014

81

10.003

10.0912

0.1958

0.0898

10.0308

0.0605

0.0004

10.5007

1.5260

11.891

01

10.388

00.0835

0.1435

1990100

0.0143

10.018

60.0134

10.0103

0.0650

0.1737

0.0979

10.1349

0.0589

0.0017

12.5370

11.228

01.5710

11.8130

0.0657

0.1493

2000110

0.0066

0.0029

0.0002

10.0045

0.0343

0.1063

0.0551

10.0947

0.0020

10.000

11

2.2010

0.3147

0.0393

11.5150

0.0952

0.1649

1970175

0.0016

0.0107

10.004

41

10.003

20.1102

0.1918

0.0768

110.007

810.049

810.000

51

0.1248

0.4727

10.490

51

10.244

00.0975

0.1797

1975180

10.003

20.0376

10.012

71

10.009

20.1234

0.2310

0.0956

110.058

710.041

310.000

61

10.221

41.3810

11.124

01

10.634

60.0806

0.1388

1980185

0.0024

0.0340

10.017

41

10.005

90.0991

0.2058

0.0920

10.0363

0.1450

0.0013

10.2055

1.4020

11.601

01

10.508

30.0974

0.1515

1985190

0.0099

0.0128

10.009

81

0.0043

0.0803

0.1770

0.0834

10.0233

10.055

410.000

41

1.0520

0.6118

10.999

61

0.4554

0.0701

0.1356

1990195

0.0212

10.039

10.0250

10.0172

0.0721

0.1870

0.1042

10.1550

0.0819

0.0025

12.4980

11.774

02.0380

12.0260

0.0616

0.1327

1995100

0.0090

0.0052

10.000

81

0.0047

0.0516

0.1429

0.0817

10.0636

10.027

20.0007

11.4770

0.3081

10.086

11

0.7763

0.0647

0.1592

2000105

0.0083

0.0048

10.000

61

0.0061

0.0351

0.1158

0.0684

10.0644

10.007

210.000

21

2.0180

0.3524

10.069

21

1.4850

0.0760

0.1482

2005110

0.0037

0.0032

10.000

11

0.0018

0.0317

0.0889

0.0310

10.1188

0.0081

0.0000

10.9908

0.3044

10.038

61

0.4708

0.1121

0.1838

193512010

0.0042

0.0111

10.003

21

0.0010

0.0799

0.1633

0.0727

10.0148

10.015

90.0000

11.5690

2.0580

11.326

01

0.3924

0.0860

0.1568

TABLE!3h

:!Value


ortfolio!!!!!!!!!+!!!!!!!5x5!Do

uble1Sort!T

est!P

ortfolios!B

uilt!Usin

g!Va


SUMMAR

Y!RE

SULTS!FO

R!TH

E!RE

GRESSION

Statistics

¯ �0

¯ � 1¯ �2

¯ � 3�0�

Rf

s(�0)

s(�

1)

s(�2)

s(�3)

⇢ 0(�

0�R

f)⇢

M(�

1)

⇢0(�

2)

⇢0(�3)

t(¯ �0)

t(¯ �1)

t(¯ �2)

t(¯ �3)

t(�0�

Rf)

r2s(

r2)

Rp

=�0t+

�1t�

p+�2t�

2 p+

�3ts p

(ei)

+⌘

p

51

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Perio

d!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!C:

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

193516/68

0.0080

0.0035

10.0195

0.0067

0.0499

0.0522

10.5454

0.0065

10.027

31

10.001

63.2130

1.3280

10.7161

2.6870

0.1051

0.1668

1935145

0.0075

0.0071

10.0223

0.0073

0.0673

0.0667

10.4140

0.0075

10.020

61

10.018

21.2720

1.2100

10.6162

1.2470

0.0932

0.1605

1946155

0.0101

0.0035

110.034

40.0092

0.0386

0.0451

10.5357

10.095

410.023

31

10.057

52.8710

0.8426

110.702

82.6030

0.1369

0.1961

195616/68

0.0068

0.0003

10.0602

0.0042

0.0391

0.0423

10.6450

0.2403

10.066

51

0.0574

2.1200

0.0927

11.1430

1.2990

0.0901

0.1427

1935140

0.0071

0.0070

110.026

30.0071

0.0829

0.0815

10.4156

10.079

010.028

41

10.012

30.7250

0.7233

110.533

60.7172

0.0784

0.1486

1941145

0.0079

0.0071

10.0798

0.0077

0.0428

0.0437

10.4080

0.0472

0.0079

110.025

51.4270

1.2620

11.5150

1.3880

0.1108

0.1732

1946150

0.0043

0.0026

10.0202

0.0036

0.0410

0.0509

10.5145

0.0447

10.019

91

10.058

70.8042

0.3995

10.3041

0.6781

0.1893

0.2055

1951155

0.0160

0.0043

110.088

90.0148

0.0355

0.0389

10.5549

10.300

710.040

71

10.056

53.4930

0.8590

111.241

03.2210

0.0845

0.1724

1956160

0.0106

10.002

11

0.0018

0.0085

0.0295

0.0352

10.5972

0.1759

0.0193

10.0236

2.7800

10.457

21

0.0235

2.2270

0.0595

0.1113

196116/68

0.0042

0.0019

10.0991

0.0013

0.0443

0.0466

10.6754

0.2387

10.101

81

0.0843

0.9017

0.3906

11.3920

0.2715

0.1106

0.1575

7/196812010

0.0088

0.0002

10.0252

0.0042

0.0450

0.0556

10.7536

0.1159

0.0642

10.0552

4.3940

0.0908

10.7537

2.1320

0.1182

0.1738

1970180

0.0082

10.004

11

0.0885

0.0028

0.0543

0.0611

11.0410

0.1243

0.0560

10.1317

1.7390

10.776

21

0.9763

0.5849

0.1343

0.1935

1980190

0.0180

10.002

31

10.028

20.0110

0.0466

0.0640

10.7171

0.0457

0.1134

10.0315

4.4460

10.410

81

10.452

52.7200

0.0947

0.1568

1990100

0.0054

0.0060

110.002

90.0013

0.0427

0.0501

10.5821

0.1626

10.024

51

0.0427

1.4480

1.3700

110.057

80.3503

0.1081

0.1589

2000110

0.0054

10.001

21

0.0714

0.0034

0.0360

0.0495

10.6482

0.1033

10.020

11

0.0233

1.7300

10.272

31

1.2650

1.0760

0.1338

0.1785

1970175

0.0096

0.0088

110.162

30.0048

0.0603

0.0643

11.0060

0.1212

0.0211

110.014

31.3500

1.1570

111.369

00.6745

0.1392

0.2076

1975180

0.0098

10.013

11

0.3125

0.0038

0.0489

0.0549

11.0290

0.0783

10.019

41

0.3051

1.6990

12.020

01

2.5760

0.6604

0.1240

0.1795

1980185

0.0198

10.008

51

0.0749

0.0114

0.0463

0.0659

10.7240

0.0758

0.1387

10.0818

3.6170

11.095

01

0.8781

2.1040

0.1061

0.1585

1985190

0.0176

0.0008

110.085

70.0120

0.0449

0.0605

10.6914

0.0032

0.0907

110.002

13.3300

0.1176

111.051

02.2710

0.0784

0.1539

1990195

0.0033

0.0071

10.0034

10.000

70.0395

0.0466

10.5454

0.0875

10.000

71

0.0181

0.7038

1.2960

10.0527

10.152

70.0932

0.1388

1995100

0.0104

0.0040

110.013

40.0061

0.0454

0.0506

10.5964

0.2356

10.044

21

0.0684

1.9460

0.6656

110.189

91.1500

0.1240

0.1766

2000105

0.0093

10.000

21

0.0425

0.0070

0.0355

0.0428

10.6850

0.0907

10.104

81

0.0354

2.2230

10.037

61

0.5264

1.6880

0.1222

0.1666

2005110

0.0005

10.003

41

0.1269

10.001

50.0339

0.0536

10.5823

0.0814

0.0112

10.0020

0.1205

10.534

71

1.8490

10.367

00.1443

0.1890

193512010

0.0084

0.0016

10.0227

0.0053

0.0472

0.0541

10.6697

0.0630

0.0271

10.0307

5.3890

0.9199

11.0220

3.4060

0.1124

0.1708

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!D:

!!

!!

!!

!!

!!

!!

!!

!!

!!

!!

193516/68

0.0010

0.0155

10.004

70.0207

10.000

30.0805

0.1478

0.0627

0.5708

10.000

910.086

410.000

40.0189

0.2507

2.0980

11.487

00.7244

10.074

10.1118

0.1779

1935145

10.004

50.0246

10.006

30.0402

10.004

70.0853

0.1463

0.0528

0.4519

10.005

110.217

810.000

610.017

710.610

31.9240

11.355

01.0180

10.629

60.0989

0.1733

1946155

0.0078

0.0075

10.001

310.039

10.0068

0.0759

0.1334

0.0538

0.5677

0.1088

0.1180

0.0001

10.036

61.1230

0.6149

10.259

710.755

10.9878

0.1498

0.2010

195616/68

0.0004

0.0139

10.006

00.0514

10.002

20.0798

0.1602

0.0762

0.6595

0.1027

10.112

110.000

60.0934

0.0665

1.0650

10.960

60.9547

10.333

40.0925

0.1575

1935140

10.002

20.0199

10.004

510.015

510.002

20.0976

0.1711

0.0583

0.4584

10.121

110.224

810.000

910.011

310.187

10.9809

10.649

210.285

310.193

70.0867

0.1645

1941145

10.007

40.0301

10.008

30.1061

10.007

60.0687

0.1112

0.0459

0.4387

10.080

510.205

810.000

310.025

710.830

72.0980

11.407

01.8740

10.856

10.1134

0.1836

1946150

10.002

60.0130

10.004

10.0347

10.003

20.0712

0.1164

0.0391

0.5499

0.0120

0.1577

0.0001

10.054

810.279

20.8645

10.805

70.4894

10.351

30.2041

0.2189

1951155

0.0181

0.0020

0.0015

10.113

00.0169

0.0797

0.1493

0.0656

0.5802

0.1486

0.0799

0.0001

10.019

71.7640

0.1028

0.1785

11.509

01.6460

0.0956

0.1660

1956160

0.0062

0.0099

10.006

210.003

60.0041

0.0542

0.1483

0.0770

0.5815

10.277

310.365

510.001

60.0314

0.8835

0.5150

10.624

210.047

60.5807

0.0631

0.1137

196116/68

10.003

40.0167

10.005

80.0881

10.006

30.0931

0.1684

0.0761

0.7076

0.1834

0.0211

0.0000

0.1386

10.346

30.9381

10.726

11.1810

10.645

70.1121

0.1788

7/196812010

0.0026

0.0106

10.004

70.0413

10.001

90.0883

0.1757

0.0836

0.7800

0.0761

0.0235

0.0004

0.0691

0.6691

1.3660

11.281

01.1960

10.491

00.1271

0.1881

1970180

10.012

40.0326

10.016

30.1144

10.017

90.1260

0.2067

0.0896

1.0980

0.0374

10.066

610.000

10.1583

11.132

01.8100

12.083

01.1970

11.629

00.1412

0.1995

1980190

0.0032

0.0262

10.014

80.0105

10.003

90.0974

0.1971

0.0929

0.7621

0.0924

0.0489

0.0007

0.0696

0.3759

1.5240

11.831

00.1589

10.457

00.1053

0.1672

1990100

0.0107

10.009

60.0088

0.0016

0.0066

0.0707

0.1797

0.0978

0.6078

0.1330

0.0908

0.0015

0.0493

1.7440

10.611

11.0320

0.0306

1.0800

0.1180

0.1863

2000110

0.0037

0.0018

10.001

00.0801

0.0017

0.0347

0.1183

0.0582

0.6299

0.0888

10.007

510.000

10.0253

1.2360

0.1761

10.193

11.4600

0.5559

0.1419

0.1930

1970175

0.0057

0.0171

10.003

210.175

80.0009

0.1160

0.1966

0.0811

1.0310

10.044

410.094

910.000

910.063

10.4163

0.7392

10.340

011.447

00.0658

0.1389

0.2085

1975180

10.023

10.0452

10.026

20.3614

10.029

10.1399

0.2287

0.1018

1.0860

0.0480

10.091

30.0002

0.3838

11.401

01.6770

12.186

02.8230

11.766

00.1403

0.1910

1980185

10.006

00.0394

10.023

50.1314

10.014

30.1070

0.2033

0.0929

0.7809

0.1144

0.1660

0.0017

0.1298

10.476

81.6430

12.149

01.4280

11.142

00.1172

0.1735

1985190

0.0154

0.0067

10.004

410.070

20.0097

0.0842

0.1809

0.0885

0.7256

0.0380

10.106

210.000

40.0280

1.5500

0.3156

10.418

910.820

60.9834

0.0927

0.1623

1990195

0.0182

10.030

40.0208

10.013

00.0142

0.0738

0.1861

0.1022

0.5515

0.1505

0.1257

0.0026

0.0221

2.0900

11.385

01.7270

10.199

31.6320

0.1066

0.1723

1995100

0.0052

0.0130

10.004

60.0120

0.0010

0.0655

0.1594

0.0851

0.6438

0.1179

0.0140

0.0003

0.0800

0.6784

0.6930

10.462

30.1580

0.1252

0.1275

0.2007

2000105

0.0062

0.0049

10.001

60.0597

0.0039

0.0355

0.1338

0.0739

0.6998

0.0771

10.022

510.000

20.0421

1.4820

0.3118

10.188

40.7234

0.9518

0.1318

0.1745

2005110

10.000

90.0000

10.001

60.1299

10.002

80.0323

0.0915

0.0292

0.5294

0.0721

0.0071

0.0000

0.0008

10.225

010.004

310.470

32.0820

10.736

80.1481

0.2119

193512010

0.0019

0.0128

10.004

70.0322

10.001

20.0849

0.1640

0.0751

0.6954

0.0580

10.016

70.0001

0.0478

0.6784

2.3500

11.892

01.3980

10.428

70.1203

0.1837

TABLE!3h

:!Value


ortfolio!!!!!!!!!+!!!!!!!5x5!Do

uble1Sort!T

est!P

ortfolios!B

uilt!Usin

g!Va


SUMMAR

Y!RE

SULTS!FO

R!TH

E!RE

GRESSION!(con

t.)

Statistics

¯ �0

¯ � 1¯ �2

¯ � 3�0�

Rf

s(�0)

s(�

1)

s(�2)

s(�3)

⇢ 0(�

0�R

f)⇢

M(�

1)

⇢0(�

2)

⇢0(�3)

t(¯ �0)

t(¯ �1)

t(¯ �2)

t(¯ �3)

t(�0�

Rf)

r2s(

r2)

Rp

=�0t+

�1t�

p+�2t�

2 p+

�3ts p

(ei)

+⌘

p

52

53

[htp]

! ! ! ! ! ! ! ! ! ! ! !! ! !

Period

1935,6/68 0.0145 0.0132 0.0043 0.0097 0.0013 0.2154 0.0701 0.0612 0.0613 ! !

1935,45 0.0201 0.0200 0.0114 0.0079 0.0001 0.2246 0.1285 0.0890 0.0890 ! !1946,55 0.0112 0.0103 0.0028 0.0089 0.0009 0.2370 0.0635 0.0434 0.0434 ! !1956,6/68 0.0122 0.0095 ,0.0007 0.0120 0.0026 0.2392 ,0.0180 0.0399 0.0400 ! !

1935,40 0.0141 0.0141 0.0084 0.0052 0.0001 0.1292 0.0776 0.1087 0.1087 ! !1941,45 0.0273 0.0270 0.0150 0.0111 0.0002 0.4669 0.2589 0.0579 0.0578 ! !1946,50 0.0077 0.0070 0.0034 0.0052 0.0007 0.1355 0.0645 0.0520 0.0520 ! !1951,55 0.0147 0.0135 0.0022 0.0126 0.0012 0.4144 0.0660 0.0326 0.0328 ! !1956,60 0.0091 0.0070 ,0.0077 0.0158 0.0021 0.2069 ,0.2268 0.0340 0.0342 ! !1961,6/68 0.0142 0.0112 0.0039 0.0094 0.0029 0.2581 0.0906 0.0435 0.0435 ! !

7/1968,2010 0.0110 0.0065 0.0009 0.0103 0.0045 0.1193 0.0170 0.0541 0.0543 ! !

1970,80 0.0116 0.0061 0.0057 0.0062 0.0055 0.0947 0.0884 0.0646 0.0647 ! !1980,90 0.0122 0.0052 ,0.0079 0.0206 0.0071 0.098 ,0.1503 0.0525 0.0528 ! !1990,00 0.0100 0.0060 0.0014 0.0096 0.0041 0.1486 0.0343 0.0401 0.0402 ! !2000,10 0.0110 0.0089 0.0022 0.0076 0.0021 0.1560 0.0393 0.0570 0.0571 ! !

1970,75 0.0036 ,0.0012 0.0017 0.0052 0.0048 ,0.0172 0.0241 0.0702 0.0704 ! !1975,80 0.0250 0.0190 0.0127 0.0093 0.0060 0.3040 0.2025 0.0625 0.0628 ! !1980,85 0.0173 0.0089 ,0.0066 0.0232 0.0083 0.185 ,0.1368 0.0483 0.0490 ! !1985,90 0.0090 0.0034 ,0.0081 0.0186 0.0056 0.061 ,0.1474 0.0548 0.0549 ! !1990,95 0.0103 0.0063 0.0014 0.0092 0.0040 0.1616 0.0359 0.0390 0.0392 ! !1995,00 0.0113 0.0070 0.0002 0.0129 0.0043 0.181 0.0064 0.0388 0.0388 ! !2000,05 0.0127 0.0104 0.0015 0.0098 0.0023 0.2474 0.0365 0.0421 0.0422 ! !2005,10 0.0087 0.0067 0.0037 0.0044 0.0019 0.1017 0.0564 0.0661 0.0662 ! !

1935,2010 0.0125 0.0094 0.0024 0.0100 0.0031 0.1642 0.0419 0.0573 0.0575 ! !

Period

1935,6/68 0.0486 0.0012 4.7400 4.309 1.5630 4.0070 ,0.0063 ,0.0040 0.0727 ,0.0002 0.9661

1935,45 0.0687 0.0002 2.5890 2.5710 1.7300 1.3130 ,0.0664 ,0.0663 0.0795 ,0.0535 0.63721946,55 0.0333 0.0004 2.8350 2.597 0.7215 2.9270 0.0875 0.0864 0.0611 0.0441 0.89231956,6/68 0.0363 0.0009 3.7290 2.926 ,0.2160 4.0390 0.1357 0.1380 0.0139 0.1317 0.8512

1935,40 0.0864 0.0002 1.0950 1.0890 0.8146 0.5032 ,0.1260 ,0.1255 0.0615 ,0.0812 0.43611941,45 0.0388 0.0001 3.6460 3.6200 1.9440 2.2130 0.1493 0.1485 0.1096 0.0961 0.72331946,50 0.0377 0.0003 1.1480 1.0510 0.5686 1.0660 0.0922 0.0898 0.0692 0.1594 0.91021951,55 0.0281 0.0004 3.5000 3.196 0.4400 3.4790 ,0.0244 ,0.0172 0.0462 ,0.1733 0.75561956,60 0.0277 0.0007 2.0840 1.592 ,2.0970 4.4140 0.1145 0.1309 0.0746 0.0870 0.65991961,6/68 0.0410 0.0008 3.0890 2.449 0.8012 2.1800 0.1318 0.1294 ,0.0197 0.1249 0.8900

7/1968,2010 0.0421 0.0025 4.5880 2.685 0.3614 5.5030 0.1864 0.1905 0.1131 0.0711 0.9605

1970,80 0.0481 0.0020 2.0600 1.086 1.0690 1.4840 0.1129 0.1148 0.1379 0.0407 0.89311980,90 0.0477 0.0023 2.6750 1.124 ,1.4340 4.9580 0.1826 0.1887 0.0575 0.0629 0.89031990,00 0.0368 0.0011 2.8790 1.702 0.3010 3.0000 0.2137 0.2177 0.1907 0.0645 0.90552000,10 0.0339 0.0016 2.2100 1.788 0.4678 2.5780 0.2689 0.2726 0.1598 ,0.0085 0.9778

1970,75 0.0541 0.0013 0.4335 ,0.146 0.2361 0.8114 0.1535 0.1577 0.0991 0.0262 0.82951975,80 0.0422 0.0023 3.3950 2.570 1.7250 1.8690 0.0478 0.0543 0.1477 0.0445 0.89641980,85 0.0511 0.0022 3.0340 1.548 ,0.9233 3.8460 0.1518 0.1729 0.0294 0.0713 0.83061985,90 0.0418 0.0010 1.3930 0.518 ,1.0900 3.7750 0.1979 0.1980 0.0789 0.0248 0.77271990,95 0.0363 0.0014 2.2370 1.364 0.2123 2.1570 0.2632 0.2685 0.2624 0.0933 0.94591995,00 0.0372 0.0005 2.4730 1.540 0.0444 2.9480 0.1544 0.1551 0.1012 0.0719 0.47972000,05 0.0357 0.0015 2.5550 2.094 0.2588 2.3310 0.1855 0.1898 ,0.0684 ,0.1138 0.97282005,10 0.0294 0.0016 1.1120 0.8607 0.5633 1.2600 0.2890 0.2927 0.3337 0.1482 0.9795

1935,2010 0.0450 0.0026 6.5970 4.941 1.2880 6.7170 0.0905 0.0962 0.0978 0.0342 0.9763

TABLE!4b:!Equal,Weighted!NYSE!Market!Portfolio!!!!!!!!!+!!!!!!!20!Single,Sort!Test!Portfolios!Built!Using!Value,Weighted!SecuritiesTHE!BEHAVIOR!OF!THE!MARKET

Statistics

Statistics

Rm Rm � Rf¯�1

¯�0 RfRm�Rf

s(Rm)

¯�1



54

[htp]

! ! ! ! ! ! ! ! ! ! ! !! ! !

Period

1935,6/68 0.0109 0.0096 0.0053 0.0077 0.0013 0.2138 0.1171 0.0449 0.0450 ! !

1935,45 0.0115 0.0114 0.0084 0.0083 0.0001 0.1899 0.1405 0.0600 0.0600 ! !1946,55 0.0123 0.0114 0.0029 0.0078 0.0009 0.3078 0.0791 0.0370 0.0370 ! !1956,6/68 0.0092 0.0066 0.0044 0.0071 0.0026 0.1925 0.1271 0.0344 0.0345 ! !

1935,40 0.0092 0.0092 0.0038 0.0082 0.0001 0.1238 0.0521 0.0739 0.0739 ! !1941,45 0.0143 0.0141 0.0139 0.0085 0.0002 0.3709 0.3656 0.0379 0.0378 ! !1946,50 0.0082 0.0075 0.0028 0.0044 0.0007 0.1819 0.0673 0.0414 0.0413 ! !1951,55 0.0165 0.0152 0.0031 0.0113 0.0012 0.4794 0.0964 0.0318 0.0319 ! !1956,60 0.0085 0.0064 ,0.0068 0.0154 0.0021 0.1905 ,0.2022 0.0337 0.0339 ! !1961,6/68 0.0097 0.0068 0.0118 0.0015 0.0029 0.1928 0.3376 0.0350 0.0351 ! !

7/1968,2010 0.0088 0.0043 0.0029 0.0082 0.0045 0.0959 0.0651 0.0444 0.0444 ! !

1970,80 0.0078 0.0023 0.0092 0.0014 0.0055 0.0478 0.1886 0.0488 0.0490 ! !1980,90 0.0130 0.0060 ,0.0050 0.0184 0.0071 0.126 ,0.1039 0.0476 0.0480 ! !1990,00 0.0123 0.0082 0.0031 0.0082 0.0041 0.2167 0.0824 0.0379 0.0379 ! !2000,10 0.0034 0.0014 0.0008 0.0088 0.0021 0.0308 0.0184 0.0443 0.0444 ! !

1970,75 0.0034 ,0.0014 0.0009 0.0045 0.0048 ,0.0271 0.0176 0.0524 0.0528 ! !1975,80 0.0157 0.0097 0.0209 ,0.0005 0.0060 0.2122 0.4569 0.0457 0.0458 ! !1980,85 0.0147 0.0064 ,0.0018 0.0193 0.0083 0.149 ,0.0412 0.0430 0.0437 ! !1985,90 0.0132 0.0076 ,0.0080 0.0192 0.0056 0.150 ,0.1585 0.0505 0.0506 ! !1990,95 0.0106 0.0067 0.0030 0.0080 0.0040 0.1986 0.0892 0.0336 0.0336 ! !1995,00 0.0163 0.0120 0.0026 0.0110 0.0043 0.302 0.0647 0.0397 0.0397 ! !2000,05 0.0032 0.0010 ,0.0001 0.0113 0.0023 0.0254 ,0.0017 0.0384 0.0385 ! !2005,10 0.0041 0.0021 0.0017 0.0059 0.0019 0.0451 0.0358 0.0471 0.0471 ! !

1935,2010 0.0097 0.0066 0.0039 0.0080 0.0031 0.1482 0.0882 0.0446 0.0447 ! !

Period

1935,6/68 0.0394 0.0012 4.8620 4.276 2.0330 3.9190 ,0.0194 ,0.0164 ,0.0114 0.1460 0.9661

1935,45 0.0545 0.0002 2.2010 2.1750 1.4060 1.7500 ,0.0815 ,0.0814 ,0.1117 0.1049 0.63721946,55 0.0259 0.0004 3.6520 3.374 0.8582 3.3180 0.0116 0.0101 0.0682 0.1404 0.89231956,6/68 0.0324 0.0009 3.2860 2.351 1.2010 2.6770 0.1149 0.1207 0.1452 0.2549 0.8512

1935,40 0.0683 0.0002 1.0520 1.0440 0.3957 1.0150 ,0.1453 ,0.1445 ,0.1948 0.0991 0.43611941,45 0.0317 0.0001 2.9180 2.8770 2.2150 2.0620 0.1957 0.1941 0.1414 0.1371 0.72331946,50 0.0312 0.0003 1.5340 1.4120 0.5097 1.1000 0.0581 0.0551 0.0334 0.2247 0.91021951,55 0.0188 0.0004 4.0120 3.699 0.7435 4.6360 ,0.1387 ,0.1314 0.0701 ,0.0566 0.75561956,60 0.0208 0.0007 1.9610 1.467 ,1.2990 5.7230 0.1006 0.1152 0.1503 0.1832 0.65991961,6/68 0.0372 0.0008 2.6250 1.827 2.4530 0.3885 0.1061 0.1064 0.0865 0.2150 0.8900

7/1968,2010 0.0385 0.0025 4.4750 2.160 1.1350 4.8140 0.0676 0.0695 0.1811 0.1388 0.9605

1970,80 0.0423 0.0020 1.8350 0.547 1.6700 0.3892 0.0239 0.0253 0.1851 0.2184 0.89311980,90 0.0424 0.0023 3.1430 1.431 ,0.9197 4.9720 0.0647 0.0750 0.2157 0.0645 0.89031990,00 0.0392 0.0011 3.7280 2.488 0.6192 2.4180 ,0.0867 ,0.0849 0.1778 0.1185 0.90552000,10 0.0308 0.0016 0.8911 0.354 0.1806 3.2810 0.1825 0.1854 0.1156 0.0324 0.9778

1970,75 0.0418 0.0013 0.5462 ,0.228 0.1332 0.9150 0.0966 0.1058 0.1544 0.1808 0.82951975,80 0.0436 0.0023 2.9150 1.797 2.6040 ,0.0968 ,0.0320 ,0.0340 0.2274 0.2510 0.89641980,85 0.0427 0.0022 2.9040 1.240 ,0.2602 3.8410 0.0511 0.0778 0.1761 0.0973 0.83061985,90 0.0406 0.0010 2.2190 1.270 ,1.0760 4.0030 0.0862 0.0844 0.2430 0.0455 0.77271990,95 0.0394 0.0014 2.6910 1.684 0.4523 1.7320 ,0.1039 ,0.1042 0.2868 0.2031 0.94591995,00 0.0382 0.0005 3.4740 2.560 0.3790 2.4320 ,0.0801 ,0.0776 0.0713 0.0530 0.47972000,05 0.0308 0.0015 0.7153 0.215 ,0.0104 3.1210 0.0366 0.0436 ,0.0400 ,0.0763 0.97282005,10 0.0294 0.0016 0.7322 0.3824 0.3031 1.6990 0.2615 0.2618 0.2953 0.1505 0.9795

1935,2010 0.0389 0.0026 6.5800 4.458 2.1570 6.2010 0.0292 0.0346 0.1083 0.1433 0.9763

TABLE!4c:!Value,Weighted!NYSE!Market!Portfolio!!!!!!!!!+!!!!!!!20!Single,Sort!Test!Portfolios!Built!Using!Equal,Weighted!SecuritiesTHE!BEHAVIOR!OF!THE!MARKET

Statistics

Statistics

Rm Rm � Rf¯�1

¯�0 RfRm�Rf

s(Rm)

¯�1



55

[hp]

! ! ! ! ! ! ! ! ! ! ! !! ! !

Period

1935,6/68 0.0109 0.0096 0.0026 0.0096 0.0013 0.2138 0.0580 0.0449 0.0450 ! !

1935,45 0.0115 0.0114 0.0088 0.0061 0.0001 0.1899 0.1464 0.0600 0.0600 ! !1946,55 0.0123 0.0114 0.0031 0.0082 0.0009 0.3078 0.0826 0.0370 0.0370 ! !1956,6/68 0.0092 0.0066 ,0.0031 0.0137 0.0026 0.1925 ,0.0915 0.0344 0.0345 ! !

1935,40 0.0092 0.0092 0.0049 0.0057 0.0001 0.1238 0.0669 0.0739 0.0739 ! !1941,45 0.0143 0.0141 0.0133 0.0066 0.0002 0.3709 0.3519 0.0379 0.0378 ! !1946,50 0.0082 0.0075 0.0048 0.0028 0.0007 0.1819 0.1157 0.0414 0.0413 ! !1951,55 0.0165 0.0152 0.0013 0.0135 0.0012 0.4794 0.0414 0.0318 0.0319 ! !1956,60 0.0085 0.0064 ,0.0071 0.0148 0.0021 0.1905 ,0.2094 0.0337 0.0339 ! !1961,6/68 0.0097 0.0068 ,0.0005 0.0130 0.0029 0.1928 ,0.0156 0.0350 0.0351 ! !

7/1968,2010 0.0088 0.0043 0.0000 0.0110 0.0045 0.0959 ,0.0003 0.0444 0.0444 ! !

1970,80 0.0078 0.0023 0.0043 0.0071 0.0055 0.0478 0.0876 0.0488 0.0490 ! !1980,90 0.0130 0.0060 ,0.0061 0.0193 0.0071 0.126 ,0.1286 0.0476 0.0480 ! !1990,00 0.0123 0.0082 0.0016 0.0096 0.0041 0.2167 0.0412 0.0379 0.0379 ! !2000,10 0.0034 0.0014 ,0.0023 0.0111 0.0021 0.0308 ,0.0530 0.0443 0.0444 ! !

1970,75 0.0034 ,0.0014 ,0.0014 0.0085 0.0048 ,0.0271 ,0.0265 0.0524 0.0528 ! !1975,80 0.0157 0.0097 0.0125 0.0074 0.0060 0.2122 0.2741 0.0457 0.0458 ! !1980,85 0.0147 0.0064 ,0.0048 0.0216 0.0083 0.149 ,0.1109 0.0430 0.0437 ! !1985,90 0.0132 0.0076 ,0.0090 0.0204 0.0056 0.150 ,0.1776 0.0505 0.0506 ! !1990,95 0.0106 0.0067 ,0.0008 0.0116 0.0040 0.1986 ,0.0228 0.0336 0.0336 ! !1995,00 0.0163 0.0120 0.0019 0.0113 0.0043 0.302 0.0488 0.0397 0.0397 ! !2000,05 0.0032 0.0010 ,0.0049 0.0162 0.0023 0.0254 ,0.1268 0.0384 0.0385 ! !2005,10 0.0041 0.0021 0.0002 0.0058 0.0019 0.0451 0.0053 0.0471 0.0471 ! !

1935,2010 0.0097 0.0066 0.0011 0.0103 0.0031 0.1482 0.0255 0.0446 0.0447 ! !

Period

1935,6/68 0.0528 0.0012 4.8620 4.276 1.1050 3.6250 ,0.0194 ,0.0164 0.0339 0.0620 0.9661

1935,45 0.0730 0.0002 2.2010 2.1750 1.7170 0.9563 ,0.0815 ,0.0814 ,0.0244 0.0108 0.63721946,55 0.0376 0.0004 3.6520 3.374 0.8448 2.3780 0.0116 0.0101 0.0870 0.0476 0.89231956,6/68 0.0410 0.0009 3.2860 2.351 ,0.9410 4.0900 0.1149 0.1207 0.0572 0.1985 0.8512

1935,40 0.0900 0.0002 1.0520 1.0440 0.6171 0.5316 ,0.1453 ,0.1445 ,0.0680 0.0149 0.43611941,45 0.0461 0.0001 2.9180 2.8770 2.2520 1.1070 0.1957 0.1941 0.0616 ,0.0083 0.72331946,50 0.0446 0.0003 1.5340 1.4120 0.8178 0.4909 0.0581 0.0551 0.0751 0.1831 0.91021951,55 0.0284 0.0004 4.0120 3.699 0.3079 3.6850 ,0.1387 ,0.1314 0.0947 ,0.2932 0.75561956,60 0.0262 0.0007 1.9610 1.467 ,1.6940 4.3790 0.1006 0.1152 0.0337 0.2703 0.65991961,6/68 0.0486 0.0008 2.6250 1.827 ,0.1127 2.5320 0.1061 0.1064 0.0581 0.1803 0.8900

7/1968,2010 0.0451 0.0025 4.4750 2.160 ,0.0062 5.4830 0.0676 0.0695 0.1031 0.0826 0.9605

1970,80 0.0531 0.0020 1.8350 0.547 0.8900 1.5290 0.0239 0.0253 0.2262 0.1086 0.89311980,90 0.0481 0.0023 3.1430 1.431 ,1.1010 4.6110 0.0647 0.0750 0.0786 0.0124 0.89031990,00 0.0377 0.0011 3.7280 2.488 0.3412 2.9220 ,0.0867 ,0.0849 0.0614 0.0904 0.90552000,10 0.0355 0.0016 0.8911 0.354 ,0.5524 3.5730 0.1825 0.1854 0.0983 0.0200 0.9778

1970,75 0.0622 0.0013 0.5462 ,0.228 ,0.2267 1.1650 0.0966 0.1058 0.2678 0.1395 0.82951975,80 0.0482 0.0023 2.9150 1.797 1.8680 1.2970 ,0.0320 ,0.0340 0.1922 0.0255 0.89641980,85 0.0486 0.0022 2.9040 1.240 ,0.6846 3.7750 0.0511 0.0778 0.0895 ,0.0047 0.83061985,90 0.0456 0.0010 2.2190 1.270 ,1.1730 3.7920 0.0862 0.0844 0.0694 0.0377 0.77271990,95 0.0349 0.0014 2.6910 1.684 ,0.1317 2.8270 ,0.1039 ,0.1042 0.0415 0.0948 0.94591995,00 0.0411 0.0005 3.4740 2.560 0.3004 2.3220 ,0.0801 ,0.0776 0.0971 0.1295 0.47972000,05 0.0323 0.0015 0.7153 0.215 ,0.9047 4.2510 0.0366 0.0436 ,0.0645 ,0.0948 0.97282005,10 0.0362 0.0016 0.7322 0.3824 0.0431 1.3580 0.2615 0.2618 0.2202 0.0796 0.9795

1935,2010 0.0486 0.0026 6.5800 4.458 0.6693 6.4180 0.0292 0.0346 0.0787 0.0716 0.9763

TABLE!4d:!Value,Weighted!NYSE!Market!Portfolio!!!!!!!!!+!!!!!!!20!Single,Sort!Test!Portfolios!Built!Using!Value,Weighted!SecuritiesTHE!BEHAVIOR!OF!THE!MARKET

Statistics

Statistics

Rm Rm � Rf¯�1

¯�0 RfRm�Rf

s(Rm)

¯�1



56

[hp]

! ! ! ! ! ! ! ! ! ! ! !! ! !

Period

1935,6/68 0.0145 0.0132 0.0086 0.0060 0.0013 0.2154 0.1408 0.0612 0.0613 ! !

1935,45 0.0201 0.0200 0.0165 0.0040 0.0001 0.2246 0.1854 0.0890 0.0890 ! !1946,55 0.0112 0.0103 0.0022 0.0090 0.0009 0.2370 0.0513 0.0434 0.0434 ! !1956,6/68 0.0122 0.0095 0.0068 0.0054 0.0026 0.2392 0.1713 0.0399 0.0400 ! !

1935,40 0.0141 0.0141 0.0119 0.0020 0.0001 0.1292 0.1097 0.1087 0.1087 ! !1941,45 0.0273 0.0270 0.0219 0.0062 0.0002 0.4669 0.3788 0.0579 0.0578 ! !1946,50 0.0077 0.0070 0.0021 0.0058 0.0007 0.1355 0.0399 0.0520 0.0520 ! !1951,55 0.0147 0.0135 0.0024 0.0123 0.0012 0.4144 0.0729 0.0326 0.0328 ! !1956,60 0.0091 0.0070 ,0.0047 0.0137 0.0021 0.2069 ,0.1389 0.0340 0.0342 ! !1961,6/68 0.0142 0.0112 0.0145 ,0.0001 0.0029 0.2581 0.3343 0.0435 0.0435 ! !

7/1968,2010 0.0110 0.0065 0.0036 0.0081 0.0045 0.1193 0.0667 0.0541 0.0543 ! !

1970,80 0.0116 0.0061 0.0093 0.0031 0.0055 0.0947 0.1445 0.0646 0.0647 ! !1980,90 0.0122 0.0052 ,0.0041 0.0172 0.0071 0.098 ,0.0778 0.0525 0.0528 ! !1990,00 0.0100 0.0060 0.0017 0.0098 0.0041 0.1486 0.0423 0.0401 0.0402 ! !2000,10 0.0110 0.0089 0.0049 0.0058 0.0021 0.1560 0.0866 0.0570 0.0571 ! !

1970,75 0.0036 ,0.0012 ,0.0008 0.0062 0.0048 ,0.0172 ,0.0114 0.0702 0.0704 ! !1975,80 0.0250 0.0190 0.0224 0.0023 0.0060 0.3040 0.3577 0.0625 0.0628 ! !1980,85 0.0173 0.0089 ,0.0004 0.0179 0.0083 0.185 ,0.0085 0.0483 0.0490 ! !1985,90 0.0090 0.0034 ,0.0076 0.0183 0.0056 0.061 ,0.1395 0.0548 0.0549 ! !1990,95 0.0103 0.0063 0.0028 0.0084 0.0040 0.1616 0.0718 0.0390 0.0392 ! !1995,00 0.0113 0.0070 0.0000 0.0136 0.0043 0.181 ,0.0011 0.0388 0.0388 ! !2000,05 0.0127 0.0104 0.0040 0.0079 0.0023 0.2474 0.0950 0.0421 0.0422 ! !2005,10 0.0087 0.0067 0.0060 0.0031 0.0019 0.1017 0.0913 0.0661 0.0662 ! !

1935,2010 0.0125 0.0094 0.0058 0.0072 0.0031 0.1642 0.1014 0.0573 0.0575 ! !

Period

1935,6/68 0.0356 0.0012 4.7400 4.309 2.6110 3.3930 ,0.0063 ,0.0040 0.0378 0.1256 0.9661

1935,45 0.0466 0.0002 2.5890 2.5710 1.9310 0.9717 ,0.0664 ,0.0663 ,0.0132 0.0826 0.63721946,55 0.0258 0.0004 2.8350 2.597 0.6220 3.8340 0.0875 0.0864 0.0758 0.0359 0.89231956,6/68 0.0310 0.0009 3.7290 2.926 1.8510 2.1460 0.1357 0.1380 0.1762 0.2518 0.8512

1935,40 0.0566 0.0002 1.0950 1.0890 0.8452 0.3024 ,0.1260 ,0.1255 ,0.0563 0.0528 0.43611941,45 0.0311 0.0001 3.6460 3.6200 2.5960 1.5510 0.1493 0.1485 0.1390 0.1884 0.72331946,50 0.0303 0.0003 1.1480 1.0510 0.3642 1.4830 0.0922 0.0898 0.0334 0.1115 0.91021951,55 0.0201 0.0004 3.5000 3.196 0.5425 4.7290 ,0.0244 ,0.0172 0.1101 ,0.1058 0.75561956,60 0.0217 0.0007 2.0840 1.592 ,1.0610 4.8830 0.1145 0.1309 0.1421 0.1404 0.65991961,6/68 0.0349 0.0008 3.0890 2.449 2.7640 ,0.0250 0.1318 0.1294 0.1426 0.2193 0.8900

7/1968,2010 0.0358 0.0025 4.5880 2.685 1.3980 5.1250 0.1864 0.1905 0.2038 0.0909 0.9605

1970,80 0.0395 0.0020 2.0600 1.086 1.6180 0.9007 0.1129 0.1148 0.2102 0.1365 0.89311980,90 0.0385 0.0023 2.6750 1.124 ,0.7994 5.1380 0.1826 0.1887 0.2295 0.0189 0.89031990,00 0.0372 0.0011 2.8790 1.702 0.3619 3.0170 0.2137 0.2177 0.2472 0.1243 0.90552000,10 0.0308 0.0016 2.2100 1.788 0.9819 2.1630 0.2689 0.2726 0.1592 0.0580 0.9778

1970,75 0.0443 0.0013 0.4335 ,0.146 ,0.1031 1.1970 0.1535 0.1577 0.1788 0.1045 0.82951975,80 0.0366 0.0023 3.3950 2.570 2.8630 0.5427 0.0478 0.0543 0.2594 0.1625 0.89641980,85 0.0350 0.0022 3.0340 1.548 ,0.0628 4.3340 0.1518 0.1729 0.1835 0.1268 0.83061985,90 0.0409 0.0010 1.3930 0.518 ,1.0840 3.7960 0.1979 0.1980 0.2593 ,0.0404 0.77271990,95 0.0377 0.0014 2.2370 1.364 0.4344 1.8860 0.2632 0.2685 0.3471 0.1780 0.94591995,00 0.0355 0.0005 2.4730 1.540 ,0.0069 3.2430 0.1544 0.1551 0.1332 0.0924 0.47972000,05 0.0323 0.0015 2.5550 2.094 0.6612 2.0640 0.1855 0.1898 0.0337 ,0.0384 0.97282005,10 0.0270 0.0016 1.1120 0.8607 0.8427 0.9688 0.2890 0.2927 0.2286 0.1837 0.9795

1935,2010 0.0357 0.0026 6.5970 4.941 2.8360 6.0890 0.0905 0.0962 0.1238 0.1088 0.9763

TABLE!4e:!Equal,Weighted!NYSE!Market!Portfolio!!!!!!!!!+!!!!!!!5x5!Double,Sort!Test!Portfolios!Built!Using!Equal,Weighted!SecuritiesTHE!BEHAVIOR!OF!THE!MARKET

Statistics

Statistics

s(�0) s(Rf ) t(Rm � Rf ) t( ¯�1) t( ¯�0) ⇢M (Rm) ⇢(Rm � Rf ) ⇢M (�1) ⇢M (�0) ⇢M (Rf )

Rm Rm � Rf¯�1

¯�0 RfRm�Rf

s(Rm)

¯�1


t(Rm)

57

[hp]

! ! ! ! ! ! ! ! ! ! ! !! ! !

Period

1935,6/68 0.0145 0.0132 0.0043 0.0096 0.0013 0.2154 0.0706 0.0612 0.0613 ! !

1935,45 0.0201 0.0200 0.0088 0.0103 0.0001 0.2246 0.0984 0.0890 0.0890 ! !1946,55 0.0112 0.0103 0.0024 0.0093 0.0009 0.2370 0.0547 0.0434 0.0434 ! !1956,6/68 0.0122 0.0095 0.0020 0.0092 0.0026 0.2392 0.0501 0.0399 0.0400 ! !

1935,40 0.0141 0.0141 0.0031 0.0098 0.0001 0.1292 0.0286 0.1087 0.1087 ! !1941,45 0.0273 0.0270 0.0154 0.0109 0.0002 0.4669 0.2667 0.0579 0.0578 ! !1946,50 0.0077 0.0070 0.0024 0.0059 0.0007 0.1355 0.0468 0.0520 0.0520 ! !1951,55 0.0147 0.0135 0.0023 0.0127 0.0012 0.4144 0.0708 0.0326 0.0328 ! !1956,60 0.0091 0.0070 ,0.0075 0.0158 0.0021 0.2069 ,0.2202 0.0340 0.0342 ! !1961,6/68 0.0142 0.0112 0.0083 0.0048 0.0029 0.2581 0.1912 0.0435 0.0435 ! !

7/1968,2010 0.0110 0.0065 0.0022 0.0092 0.0045 0.1193 0.0410 0.0541 0.0543 ! !

1970,80 0.0116 0.0061 0.0052 0.0069 0.0055 0.0947 0.0809 0.0646 0.0647 ! !1980,90 0.0122 0.0052 ,0.0025 0.0155 0.0071 0.098 ,0.0472 0.0525 0.0528 ! !1990,00 0.0100 0.0060 0.0017 0.0096 0.0041 0.1486 0.0427 0.0401 0.0402 ! !2000,10 0.0110 0.0089 0.0034 0.0067 0.0021 0.1560 0.0597 0.0570 0.0571 ! !

1970,75 0.0036 ,0.0012 0.0002 0.0066 0.0048 ,0.0172 0.0026 0.0702 0.0704 ! !1975,80 0.0250 0.0190 0.0140 0.0086 0.0060 0.3040 0.2238 0.0625 0.0628 ! !1980,85 0.0173 0.0089 ,0.0024 0.0190 0.0083 0.185 ,0.0491 0.0483 0.0490 ! !1985,90 0.0090 0.0034 ,0.0023 0.0135 0.0056 0.061 ,0.0419 0.0548 0.0549 ! !1990,95 0.0103 0.0063 0.0017 0.0096 0.0040 0.1616 0.0439 0.0390 0.0392 ! !1995,00 0.0113 0.0070 0.0013 0.0120 0.0043 0.181 0.0348 0.0388 0.0388 ! !2000,05 0.0127 0.0104 0.0033 0.0089 0.0023 0.2474 0.0783 0.0421 0.0422 ! !2005,10 0.0087 0.0067 0.0039 0.0038 0.0019 0.1017 0.0595 0.0661 0.0662 ! !

1935,2010 0.0125 0.0094 0.0031 0.0094 0.0031 0.1642 0.0548 0.0573 0.0575 ! !

Period

1935,6/68 0.0451 0.0012 4.7400 4.309 1.5860 4.2460 ,0.0063 ,0.0040 0.0187 0.0245 0.9661

1935,45 0.0610 0.0002 2.5890 2.5710 1.3600 1.9250 ,0.0664 ,0.0663 ,0.0448 ,0.0206 0.63721946,55 0.0344 0.0004 2.8350 2.597 0.6019 2.9550 0.0875 0.0864 0.0653 ,0.0507 0.89231956,6/68 0.0356 0.0009 3.7290 2.926 0.5888 3.1590 0.1357 0.1380 0.1328 0.1961 0.8512

1935,40 0.0751 0.0002 1.0950 1.0890 0.2986 1.0940 ,0.1260 ,0.1255 ,0.1066 ,0.0574 0.43611941,45 0.0389 0.0001 3.6460 3.6200 2.2810 2.1680 0.1493 0.1485 0.1098 0.1410 0.72331946,50 0.0389 0.0003 1.1480 1.0510 0.3969 1.1660 0.0922 0.0898 0.0703 0.0556 0.91021951,55 0.0291 0.0004 3.5000 3.196 0.4617 3.3760 ,0.0244 ,0.0172 0.0543 ,0.2054 0.75561956,60 0.0283 0.0007 2.0840 1.592 ,1.8320 4.3280 0.1145 0.1309 0.0255 0.0416 0.65991961,6/68 0.0393 0.0008 3.0890 2.449 1.7110 1.1500 0.1318 0.1294 0.1292 0.2139 0.8900

7/1968,2010 0.0378 0.0025 4.5880 2.685 0.9199 5.5070 0.1864 0.1905 0.1277 0.0542 0.9605

1970,80 0.0451 0.0020 2.0600 1.086 0.9262 1.7450 0.1129 0.1148 0.1182 0.0264 0.89311980,90 0.0401 0.0023 2.6750 1.124 ,0.5050 4.4530 0.1826 0.1887 0.0502 0.0291 0.89031990,00 0.0346 0.0011 2.8790 1.702 0.4184 3.1920 0.2137 0.2177 0.2096 0.0428 0.90552000,10 0.0310 0.0016 2.2100 1.788 0.7671 2.4690 0.2689 0.2726 0.1848 0.0715 0.9778

1970,75 0.0510 0.0013 0.4335 ,0.146 0.0239 1.0990 0.1535 0.1577 0.0970 0.0545 0.82951975,80 0.0394 0.0023 3.3950 2.570 1.7360 1.8570 0.0478 0.0543 0.1436 ,0.0767 0.89641980,85 0.0398 0.0022 3.0340 1.548 ,0.3824 4.0550 0.1518 0.1729 0.0138 0.0661 0.83061985,90 0.0387 0.0010 1.3930 0.518 ,0.3381 2.9610 0.1979 0.1980 0.0853 ,0.0330 0.77271990,95 0.0319 0.0014 2.2370 1.364 0.3107 2.5510 0.2632 0.2685 0.2612 0.0390 0.94591995,00 0.0368 0.0005 2.4730 1.540 0.2483 2.7660 0.1544 0.1551 0.1688 0.0738 0.47972000,05 0.0327 0.0015 2.5550 2.094 0.6270 2.3010 0.1855 0.1898 0.0282 0.0229 0.97282005,10 0.0272 0.0016 1.1120 0.8607 0.6140 1.1990 0.2890 0.2927 0.2791 0.1310 0.9795

1935,2010 0.0411 0.0026 6.5970 4.941 1.7420 6.8720 0.0905 0.0962 0.0815 0.0395 0.9763

TABLE!4f:!Equal,Weighted!NYSE!Market!Portfolio!!!!!!!!!+!!!!!!!5x5!Double,Sort!Test!Portfolios!Built!Using!Value,Weighted!SecuritiesTHE!BEHAVIOR!OF!THE!MARKET

Statistics

Statistics

Rm Rm � Rf¯�1

¯�0 RfRm�Rf

s(Rm)

¯�1



58

[hp]

! ! ! ! ! ! ! ! ! ! ! !! ! !

Period

1935,6/68 0.0109 0.0096 0.0071 0.0053 0.0013 0.2138 0.1583 0.0449 0.0450 ! !

1935,45 0.0115 0.0114 0.0123 0.0029 0.0001 0.1899 0.2052 0.0600 0.0600 ! !1946,55 0.0123 0.0114 0.0028 0.0080 0.0009 0.3078 0.0770 0.0370 0.0370 ! !1956,6/68 0.0092 0.0066 0.0060 0.0053 0.0026 0.1925 0.1742 0.0344 0.0345 ! !

1935,40 0.0092 0.0092 0.0085 0.0017 0.0001 0.1238 0.1150 0.0739 0.0739 ! !1941,45 0.0143 0.0141 0.0168 0.0042 0.0002 0.3709 0.4442 0.0379 0.0378 ! !1946,50 0.0082 0.0075 0.0027 0.0046 0.0007 0.1819 0.0646 0.0414 0.0413 ! !1951,55 0.0165 0.0152 0.0030 0.0114 0.0012 0.4794 0.0949 0.0318 0.0319 ! !1956,60 0.0085 0.0064 ,0.0061 0.0146 0.0021 0.1905 ,0.1800 0.0337 0.0339 ! !1961,6/68 0.0097 0.0068 0.0140 ,0.0009 0.0029 0.1928 0.4003 0.0350 0.0351 ! !

7/1968,2010 0.0088 0.0043 0.0034 0.0077 0.0045 0.0959 0.0771 0.0444 0.0444 ! !

1970,80 0.0078 0.0023 0.0100 0.0005 0.0055 0.0478 0.2055 0.0488 0.0490 ! !1980,90 0.0130 0.0060 ,0.0048 0.0183 0.0071 0.126 ,0.1016 0.0476 0.0480 ! !1990,00 0.0123 0.0082 0.0030 0.0084 0.0041 0.2167 0.0780 0.0379 0.0379 ! !2000,10 0.0034 0.0014 0.0027 0.0069 0.0021 0.0308 0.0606 0.0443 0.0444 ! !

1970,75 0.0034 ,0.0014 ,0.0008 0.0065 0.0048 ,0.0271 ,0.0161 0.0524 0.0528 ! !1975,80 0.0157 0.0097 0.0234 ,0.0033 0.0060 0.2122 0.5114 0.0457 0.0458 ! !1980,85 0.0147 0.0064 ,0.0005 0.0179 0.0083 0.149 ,0.0116 0.0430 0.0437 ! !1985,90 0.0132 0.0076 ,0.0089 0.0202 0.0056 0.150 ,0.1767 0.0505 0.0506 ! !1990,95 0.0106 0.0067 0.0027 0.0084 0.0040 0.1986 0.0801 0.0336 0.0336 ! !1995,00 0.0163 0.0120 0.0026 0.0108 0.0043 0.302 0.0656 0.0397 0.0397 ! !2000,05 0.0032 0.0010 0.0018 0.0094 0.0023 0.0254 0.0467 0.0384 0.0385 ! !2005,10 0.0041 0.0021 0.0039 0.0036 0.0019 0.0451 0.0820 0.0471 0.0471 ! !

1935,2010 0.0097 0.0066 0.0050 0.0066 0.0031 0.1482 0.1131 0.0446 0.0447 ! !

Period

1935,6/68 0.0371 0.0012 4.8620 4.276 2.6130 2.8610 ,0.0194 ,0.0164 0.0385 0.1187 0.9661

1935,45 0.0482 0.0002 2.2010 2.1750 1.9300 0.6796 ,0.0815 ,0.0814 ,0.0447 0.0382 0.63721946,55 0.0260 0.0004 3.6520 3.374 0.8473 3.3650 0.0116 0.0101 0.0727 0.0774 0.89231956,6/68 0.0334 0.0009 3.2860 2.351 1.5620 1.9360 0.1149 0.1207 0.1807 0.2817 0.8512

1935,40 0.0571 0.0002 1.0520 1.0440 0.8214 0.2566 ,0.1453 ,0.1445 ,0.1096 ,0.0111 0.43611941,45 0.0353 0.0001 2.9180 2.8770 2.5150 0.9199 0.1957 0.1941 0.1567 0.1897 0.72331946,50 0.0312 0.0003 1.5340 1.4120 0.4984 1.1400 0.0581 0.0551 0.0352 0.1512 0.91021951,55 0.0191 0.0004 4.0120 3.699 0.7384 4.6160 ,0.1387 ,0.1314 0.0893 ,0.0670 0.75561956,60 0.0190 0.0007 1.9610 1.467 ,1.2630 5.9630 0.1006 0.1152 0.1473 0.3042 0.65991961,6/68 0.0392 0.0008 2.6250 1.827 2.6030 ,0.2290 0.1061 0.1064 0.1437 0.2186 0.8900

7/1968,2010 0.0395 0.0025 4.4750 2.160 1.3050 4.3780 0.0676 0.0695 0.1968 0.1329 0.9605

1970,80 0.0472 0.0020 1.8350 0.547 1.7260 0.1312 0.0239 0.0253 0.2249 0.2053 0.89311980,90 0.0434 0.0023 3.1430 1.431 ,0.8950 4.8320 0.0647 0.0750 0.2373 0.0780 0.89031990,00 0.0386 0.0011 3.7280 2.488 0.5882 2.4910 ,0.0867 ,0.0849 0.1857 0.1143 0.90552000,10 0.0299 0.0016 0.8911 0.354 0.5685 2.6400 0.1825 0.1854 0.1263 0.0712 0.9778

1970,75 0.0490 0.0013 0.5462 ,0.228 ,0.1130 1.1310 0.0966 0.1058 0.2010 0.1290 0.82951975,80 0.0464 0.0023 2.9150 1.797 2.8700 ,0.5987 ,0.0320 ,0.0340 0.2614 0.2718 0.89641980,85 0.0423 0.0022 2.9040 1.240 ,0.0727 3.5900 0.0511 0.0778 0.2079 0.1734 0.83061985,90 0.0434 0.0010 2.2190 1.270 ,1.1950 3.9500 0.0862 0.0844 0.2491 ,0.0047 0.77271990,95 0.0381 0.0014 2.6910 1.684 0.4138 1.8670 ,0.1039 ,0.1042 0.2861 0.1994 0.94591995,00 0.0388 0.0005 3.4740 2.560 0.3781 2.3620 ,0.0801 ,0.0776 0.0906 0.0507 0.47972000,05 0.0299 0.0015 0.7153 0.215 0.2794 2.6650 0.0366 0.0436 ,0.0084 ,0.0592 0.97282005,10 0.0280 0.0016 0.7322 0.3824 0.6466 1.0880 0.2615 0.2618 0.2612 0.2149 0.9795

1935,2010 0.0385 0.0026 6.5800 4.458 2.6640 5.1950 0.0292 0.0346 0.1364 0.1306 0.9763

TABLE!4g:!Value,Weighted!NYSE!Market!Portfolio!!!!!!!!!+!!!!!!!5x5!Double,Sort!Test!Portfolios!Built!Using!Equal,Weighted!SecuritiesTHE!BEHAVIOR!OF!THE!MARKET

Statistics

Statistics

Rm Rm � Rf¯�1

¯�0 RfRm�Rf

s(Rm)

¯�1



59

!!

!!

!!

!

Perio

dPe

riod

!!

!!

!!

!!

!Pane

l!A!

!!

!!

!!

!Pane

l!C!

!!

!!

!!

!193516/68

0.0013

0.0011

0.0024

2.1600

0.0020

0.0010

0.0030

3.0010

193516/68

0.0014

0.0017

0.0031

1.8390

0.0015

0.0032

0.0048

1.4640

1935145

0.0026

0.0021

0.0047

2.2150

0.0038

0.0019

0.0057

2.9390

1935145

0.0030

0.0028

0.0058

2.0750

0.0021

0.0059

0.0079

1.3510

1946155

0.0006

0.0005

0.0011

2.2090

0.0013

0.0004

0.0017

3.9120

1946155

0.0010

0.0008

0.0018

2.2930

0.0021

0.0018

0.0038

2.1950

195616/68

0.0007

0.0007

0.0013

2.0110

0.0010

0.0006

0.0017

2.6040

195616/68

0.0004

0.0015

0.0019

1.2840

0.0006

0.0021

0.0027

1.2600

1935140

0.0045

0.0030

0.0075

2.5300

0.0049

0.0027

0.0076

2.7700

1935140

0.0046

0.0035

0.0081

2.3340

0.0030

0.0079

0.0109

1.3830

1941145

0.0004

0.0012

0.0015

1.3070

0.0026

0.0010

0.0036

3.5550

1941145

0.0011

0.0020

0.0032

1.5630

0.0008

0.0035

0.0043

1.2380

1946150

0.0010

0.0004

0.0014

3.1630

0.0017

0.0004

0.0021

5.2430

1946150

0.0015

0.0007

0.0022

3.1410

0.0022

0.0021

0.0043

2.0610

1951155

0.0002

0.0006

0.0008

1.4210

0.0009

0.0005

0.0014

2.9010

1951155

0.0005

0.0008

0.0013

1.6000

0.0020

0.0014

0.0034

2.4240

1956160

0.0003

0.0005

0.0008

1.5090

0.0004

0.0004

0.0008

1.8180

1956160

10.000

20.0014

0.0012

0.8514

0.0000

0.0016

0.0016

1.0170

196116/68

0.0009

0.0008

0.0017

2.2330

0.0014

0.0008

0.0022

2.8590

196116/68

0.0009

0.0015

0.0024

1.5730

0.0008

0.0025

0.0033

1.3060

7/196812010

0.0009

0.0009

0.0018

1.9740

0.0023

0.0009

0.0033

3.5070

7/196812010

0.0009

0.0017

0.0026

1.5160

0.0031

0.0040

0.0071

1.7690

1970180

0.0013

0.0010

0.0023

2.3560

0.0027

0.0010

0.0038

3.5930

1970180

0.0014

0.0020

0.0035

1.7090

0.0009

0.0056

0.0065

1.1640

1980190

0.0011

0.0012

0.0023

1.9120

0.0027

0.0013

0.0040

3.1600

1980190

0.0007

0.0019

0.0026

1.3840

0.0061

0.0041

0.0102

2.4690

1990100

0.0004

0.0010

0.0014

1.3980

0.0017

0.0010

0.0028

2.7230

1990100

0.0005

0.0015

0.0020

1.3090

0.0023

0.0027

0.0050

1.8330

2000110

0.0006

0.0005

0.0011

2.0970

0.0025

0.0005

0.0030

5.6550

2000110

0.0007

0.0015

0.0022

1.4890

0.0033

0.0037

0.0070

1.8940

1970175

0.0018

0.0012

0.0029

2.5430

0.0025

0.0012

0.0037

3.1090

1970175

0.0020

0.0022

0.0042

1.9010

0.0019

0.0063

0.0081

1.2950

1975180

0.0009

0.0009

0.0018

1.9780

0.0029

0.0010

0.0039

3.9670

1975180

0.0007

0.0021

0.0027

1.3300

10.000

20.0051

0.0049

0.9657

1980185

0.0017

0.0009

0.0026

2.8820

0.0027

0.0010

0.0037

3.8110

1980185

0.0010

0.0016

0.0026

1.6140

0.0055

0.0035

0.0090

2.5680

1985190

0.0004

0.0014

0.0018

1.2890

0.0025

0.0014

0.0039

2.7440

1985190

0.0004

0.0020

0.0024

1.2030

0.0065

0.0045

0.0110

2.4510

1990195

0.0001

0.0012

0.0013

1.0920

0.0019

0.0013

0.0031

2.4560

1990195

0.0003

0.0016

0.0019

1.1960

0.0017

0.0029

0.0045

1.5820

1995100

0.0008

0.0006

0.0014

2.2380

0.0016

0.0006

0.0023

3.5780

1995100

0.0007

0.0013

0.0021

1.5590

0.0024

0.0024

0.0048

1.9980

2000105

0.0007

0.0006

0.0013

2.3110

0.0020

0.0006

0.0025

4.6180

2000105

0.0010

0.0015

0.0025

1.6920

0.0040

0.0029

0.0069

2.4200

2005110

0.0004

0.0005

0.0009

1.7900

0.0027

0.0005

0.0032

6.8350

2005110

0.0002

0.0013

0.0015

1.1550

0.0021

0.0042

0.0063

1.5030

193512010

0.0010

0.0010

0.0020

2.0630

0.0022

0.0010

0.0032

3.2740

193512010

0.0011

0.0017

0.0028

1.6560

0.0024

0.0037

0.0061

1.6490

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!B!

!!

!!

!!

!Pane

l!D!

!!

!!

!!

!193516/68

0.0009

0.0046

0.0055

1.1890

0.0023

0.0205

0.0228

1.1130

193516/68

0.0015

0.0071

0.0085

1.2080

0.0024

0.0218

0.0242

1.1120

1935145

0.0017

0.0061

0.0079

1.2840

0.0000

0.0296

0.0296

1.0010

1935145

0.0043

0.0094

0.0137

1.4560

0.0036

0.0317

0.0353

1.1140

1946155

0.0003

0.0029

0.0032

1.1020

0.0051

0.0113

0.0164

1.4510

1946155

10.000

70.0043

0.0036

0.8340

0.0037

0.0114

0.0152

1.3280

195616/68

0.0006

0.0046

0.0053

1.1380

0.0024

0.0200

0.0224

1.1200

195616/68

0.0008

0.0072

0.0081

1.1180

0.0007

0.0214

0.0221

1.0310

1935140

0.0043

0.0078

0.0121

1.5520

0.0058

0.0344

0.0402

1.1700

1935140

0.0097

0.0112

0.0209

1.8690

0.0143

0.0372

0.0515

1.3840

1941145

10.001

20.0041

0.0029

0.7112

10.006

60.0239

0.0173

0.7231

1941145

10.002

10.0072

0.0052

0.7131

10.008

60.0251

0.0165

0.6582

1946150

0.0006

0.0019

0.0026

1.3190

0.0073

0.0073

0.0146

2.0010

1946150

0.0000

0.0036

0.0036

0.9976

0.0064

0.0074

0.0138

1.8550

1951155

0.0000

0.0038

0.0039

1.0040

0.0032

0.0153

0.0185

1.2070

1951155

10.001

40.0050

0.0036

0.7264

0.0014

0.0154

0.0168

1.0900

1956160

0.0000

0.0021

0.0022

1.0200

0.0026

0.0089

0.0115

1.2890

1956160

0.0001

0.0035

0.0036

1.0290

0.0016

0.0100

0.0116

1.1620

196116/68

0.0011

0.0063

0.0074

1.1710

0.0024

0.0273

0.0297

1.0890

196116/68

0.0014

0.0097

0.0111

1.1410

0.0002

0.0291

0.0293

1.0080

7/196812010

0.0011

0.0053

0.0064

1.1980

0.0088

0.0278

0.0366

1.3180

7/196812010

0.0015

0.0069

0.0083

1.2140

0.0070

0.0311

0.0381

1.2250

1970180

0.0012

0.0090

0.0103

1.1340

0.0051

0.0433

0.0485

1.1180

1970180

0.0026

0.0112

0.0138

1.2360

10.002

20.0501

0.0478

0.9552

1980190

0.0034

0.0067

0.0100

1.5040

0.0285

0.0319

0.0604

1.8940

1980190

0.0040

0.0083

0.0124

1.4840

0.0298

0.0341

0.0639

1.8720

1990100

10.000

90.0040

0.0032

0.7832

10.004

00.0288

0.0247

0.8595

1990100

10.000

80.0051

0.0044

0.8513

10.004

20.0307

0.0265

0.8641

2000110

0.0000

0.0014

0.0015

1.0200

0.0055

0.0082

0.0136

1.6710

2000110

10.000

30.0030

0.0026

0.8837

0.0067

0.0105

0.0172

1.6430

1970175

0.0014

0.0098

0.0112

1.1390

10.004

00.0478

0.0437

0.9154

1970175

0.0032

0.0130

0.0162

1.2500

10.005

70.0507

0.0450

0.8868

1975180

0.0019

0.0083

0.0102

1.2280

0.0144

0.0394

0.0537

1.3650

1975180

0.0024

0.0093

0.0116

1.2540

0.0015

0.0507

0.0522

1.0290

1980185

0.0031

0.0068

0.0100

1.4590

0.0232

0.0301

0.0533

1.7700

1980185

0.0037

0.0086

0.0123

1.4330

0.0223

0.0310

0.0533

1.7190

1985190

0.0041

0.0060

0.0101

1.6910

0.0355

0.0309

0.0664

2.1480

1985190

0.0053

0.0075

0.0128

1.7100

0.0393

0.0340

0.0734

2.1560

1990195

10.002

00.0061

0.0040

0.6630

10.010

10.0435

0.0334

0.7687

1990195

10.001

30.0072

0.0058

0.8158

10.011

70.0451

0.0333

0.7394

1995100

0.0007

0.0015

0.0022

1.4330

0.0037

0.0106

0.0144

1.3520

1995100

0.0004

0.0026

0.0030

1.1400

0.0049

0.0126

0.0175

1.3900

2000105

10.000

20.0015

0.0012

0.8499

10.001

10.0092

0.0081

0.8852

2000105

10.000

30.0029

0.0027

0.9119

0.0029

0.0108

0.0137

1.2660

2005110

0.0003

0.0013

0.0016

1.2470

0.0113

0.0063

0.0176

2.7900

2005110

10.000

50.0027

0.0022

0.8251

0.0097

0.0090

0.0187

2.0870

193512010

0.0010

0.0050

0.0060

1.1930

0.0059

0.0246

0.0305

1.2420

193512010

0.0015

0.0069

0.0084

1.2110

0.0050

0.0270

0.0319

1.1840

TABLE!5b

:!Equ

al1W



ortfolios!B

uilt!Usin

g!Va


COMPO

NEN

TS!OF!TH

E!VA

RIAN

CES!OF!TH

E

FF

FF

s2(�

0)

s2(�

0)

s2(�

0)

s2(�

1)

s2(�

1)

s2(�

1)

s2(�

0)

s2(�

0)

s2(�

0)

s2(�

1)

s2(�

1)

s2(�

1)

�j,

t

60

Perio

d! Pane

l!A!

!!

!!

!!

!Pane

l!C!

!!

!!

!!

!193516/68

11

11

11

11

193516/68

11

11

0.1083

0.7801

0.8884

1.1390

1935145

11

11

11

11

1935145

11

11

0.2241

0.5135

0.7376

1.4360

1946155

11

11

11

11

1946155

11

11

0.2575

0.5563

0.8138

1.4630

195616/68

11

11

11

11

195616/68

11

11

10.106

01.1920

1.0860

0.9110

1935140

11

11

11

11

1935140

11

11

0.0546

0.4053

0.4599

1.1350

1941145

11

11

11

11

1941145

11

11

0.4243

0.6415

1.0660

1.6610

1946150

11

11

11

11

1946150

11

11

0.1558

0.5227

0.6785

1.2980

1951155

11

11

11

11

1951155

11

11

0.3692

0.5900

0.9592

1.6260

1956160

11

11

11

11

1956160

11

11

10.042

21.2300

1.1880

0.9657

196116/68

11

11

11

11

196116/68

11

11

10.162

71.1660

1.0030

0.8605

7/196812010

11

11

11

11

7/196812010

11

11

0.2134

1.0800

1.2940

1.1980

1970180

11

11

11

11

1970180

11

11

0.0525

1.5110

1.5640

1.0350

1980190

11

11

11

11

1980190

11

11

0.4749

0.9183

1.3930

1.5170

1990100

11

11

11

11

1990100

11

11

0.2312

0.5972

0.8284

1.3870

2000110

11

11

11

11

2000110

11

11

0.1349

1.2010

1.3360

1.1120

1970175

11

11

11

11

1970175

11

11

0.0708

1.8280

1.8980

1.0390

1975180

11

11

11

11

1975180

11

11

10.218

31.2770

1.0590

0.8291

1980185

11

11

11

11

1980185

11

11

0.2333

0.7890

1.0220

1.2960

1985190

11

11

11

11

1985190

11

11

0.7624

1.0030

1.7650

1.7600

1990195

11

11

11

11

1990195

11

11

0.2451

0.5037

0.7488

1.4870

1995100

11

11

11

11

1995100

11

11

0.1108

0.6836

0.7944

1.1620

2000105

11

11

11

11

2000105

11

11

0.5375

0.9037

1.4410

1.5950

2005110

11

11

11

11

2005110

11

11

10.307

41.3750

1.0680

0.7764

193512010

11

11

11

11

193512010

11

11

0.1661

0.9481

1.1140

1.1750

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!B!

!!

!!

!!

!Pane

l!D!

!!

!!

!!

!193516/68

10.000

50.0047

0.0042

0.8929

11

11

193516/68

10.000

70.0058

0.0052

0.8873

0.0826

0.9386

1.0210

1.0880

1935145

10.001

90.0074

0.0055

0.7425

11

11

1935145

10.001

50.0096

0.0081

0.8469

0.3045

0.6806

0.9851

1.4470

1946155

0.0006

0.0023

0.0028

1.2540

11

11

1946155

10.000

20.0026

0.0024

0.9277

0.0321

0.7005

0.7326

1.0460

195616/68

10.000

10.0044

0.0043

0.9769

11

11

195616/68

10.000

30.0051

0.0049

0.9465

10.065

81.3550

1.2890

0.9514

1935140

10.002

30.0083

0.0060

0.7227

11

11

1935140

10.000

20.0112

0.0110

0.9828

0.3079

0.6029

0.9108

1.5110

1941145

10.001

40.0063

0.0049

0.7854

11

11

1941145

10.002

90.0078

0.0049

0.6289

0.2962

0.7724

1.0690

1.3830

1946150

0.0009

0.0013

0.0022

1.6580

11

11

1946150

0.0004

0.0017

0.0021

1.2200

10.188

30.7424

0.5541

0.7464

1951155

0.0003

0.0032

0.0035

1.0970

11

11

1951155

10.000

70.0035

0.0028

0.7930

0.2624

0.6587

0.9210

1.3980

1956160

0.0003

0.0019

0.0022

1.1510

11

11

1956160

0.0004

0.0021

0.0025

1.2050

0.0470

1.2950

1.3420

1.0360

196116/68

10.000

40.0061

0.0057

0.9381

11

11

196116/68

10.000

80.0072

0.0064

0.8933

10.157

91.3940

1.2360

0.8867

7/196812010

0.0013

0.0073

0.0086

1.1830

11

11

7/196812010

0.0014

0.0079

0.0093

1.1730

0.1814

1.1700

1.3510

1.1550

1970180

10.000

10.0104

0.0103

0.9905

11

11

1970180

10.000

30.0112

0.0109

0.9724

0.0476

1.6590

1.7070

1.0290

1980190

0.0076

0.0080

0.0156

1.9460

11

11

1980190

0.0085

0.0089

0.0174

1.9540

0.4857

0.9530

1.4390

1.5100

1990100

10.002

20.0095

0.0073

0.7666

11

11

1990100

10.002

10.0103

0.0082

0.7964

0.2405

0.6648

0.9052

1.3620

2000110

0.0004

0.0021

0.0025

1.1940

11

11

2000110

0.0003

0.0023

0.0026

1.1500

0.0468

1.3190

1.3650

1.0350

1970175

10.001

40.0115

0.0101

0.8809

11

11

1970175

10.001

30.0126

0.0113

0.9000

0.1185

2.0250

2.1430

1.0580

1975180

0.0018

0.0094

0.0112

1.1860

11

11

1975180

0.0010

0.0101

0.0111

1.1040

10.273

31.3550

1.0820

0.7983

1980185

0.0058

0.0068

0.0126

1.8450

11

11

1980185

0.0063

0.0073

0.0136

1.8590

0.3224

0.8253

1.1480

1.3910

1985190

0.0097

0.0084

0.0181

2.1460

11

11

1985190

0.0112

0.0096

0.0208

2.1720

0.7493

1.0240

1.7740

1.7310

1990195

10.004

50.0146

0.0102

0.6952

11

11

1990195

10.003

90.0157

0.0118

0.7506

0.3753

0.5633

0.9386

1.6660

1995100

0.0006

0.0032

0.0039

1.1900

11

11

1995100

0.0004

0.0035

0.0040

1.1240

0.0397

0.7500

0.7897

1.0530

2000105

10.000

20.0026

0.0024

0.9255

11

11

2000105

10.000

10.0027

0.0026

0.9536

0.5223

1.0160

1.5380

1.5140

2005110

0.0009

0.0014

0.0023

1.6590

11

11

2005110

0.0007

0.0016

0.0023

1.4530

10.445

51.4890

1.0430

0.7008

193512010

0.0005

0.0062

0.0067

1.0840

11

11

193512010

0.0005

0.0070

0.0075

1.0670

0.1382

1.0680

1.2060

1.1290

FF

FF

TABLE!5b

:!Equ

al1W



ortfolios!B

uilt!Usin

g!Va


COMPO

NEN

TS!OF!TH

E!VA

RIAN

CES!OF!TH

E!!!!!!!!!!!!!(con

t.)

s2(�

2)

s2(�

2)

s2(�

2)

s2(�

3)

s2(�

3)

s2(�

3)

s2(�

2)

s2(�

2)

s2(�

2)

s2(�

3)

s2(�

3)

s2(�

3)

�j,

t

61

!!

!!

!!

!

Perio

dPe

riod

!!

!!

!!

!!

!Pane

l!A!

!!

!!

!!

!Pane

l!C!

!!

!!

!!

!193516/68

0.0012

0.0003

0.0016

4.6250

11

11

193516/68

0.0016

0.0009

0.0025

2.9090

0.0020

0.0007

0.0027

3.6870

1935145

0.0022

0.0007

0.0030

4.0150

11

11

1935145

0.0033

0.0017

0.0050

2.8770

0.0029

0.0010

0.0039

3.9210

1946155

0.0006

0.0001

0.0007

6.4080

11

11

1946155

0.0008

0.0001

0.0009

6.5630

0.0015

0.0004

0.0019

4.8850

195616/68

0.0009

0.0002

0.0010

6.1890

11

11

195616/68

0.0009

0.0007

0.0016

2.3900

0.0015

0.0008

0.0023

2.9820

1935140

0.0036

0.0011

0.0047

4.2570

11

11

1935140

0.0048

0.0027

0.0074

2.7870

0.0044

0.0011

0.0055

4.9550

1941145

0.0007

0.0003

0.0010

3.1690

11

11

1941145

0.0016

0.0007

0.0023

3.4080

0.0011

0.0008

0.0020

2.3700

1946150

0.0009

0.0001

0.0010

8.6930

11

11

1946150

0.0011

0.0001

0.0012

8.8920

0.0019

0.0005

0.0024

5.1940

1951155

0.0003

0.0001

0.0004

3.6400

11

11

1951155

0.0005

0.0002

0.0007

4.3910

0.0012

0.0003

0.0015

4.5610

1956160

0.0003

0.0001

0.0004

3.6440

11

11

1956160

0.0006

0.0004

0.0010

2.4940

0.0008

0.0009

0.0017

1.8870

196116/68

0.0012

0.0002

0.0014

6.8490

11

11

196116/68

0.0010

0.0008

0.0019

2.2550

0.0020

0.0007

0.0027

3.8870

7/196812010

0.0012

0.0002

0.0015

6.2740

11

11

7/196812010

0.0016

0.0006

0.0021

3.7690

0.0038

0.0013

0.0051

3.9110

1970180

0.0015

0.0003

0.0018

5.5880

11

11

1970180

0.0020

0.0005

0.0025

5.0050

0.0039

0.0014

0.0053

3.8160

1980190

0.0015

0.0003

0.0018

6.5230

11

11

1980190

0.0017

0.0005

0.0022

4.8200

0.0055

0.0017

0.0073

4.1870

1990100

0.0013

0.0003

0.0015

5.5980

11

11

1990100

0.0014

0.0005

0.0019

3.8290

0.0023

0.0014

0.0037

2.6900

2000110

0.0008

0.0001

0.0010

6.8390

11

11

2000110

0.0011

0.0009

0.0020

2.2300

0.0046

0.0012

0.0058

4.8080

1970175

0.0014

0.0004

0.0017

4.8900

11

11

1970175

0.0021

0.0007

0.0028

4.1670

0.0030

0.0011

0.0041

3.6640

1975180

0.0016

0.0003

0.0019

5.9210

11

11

1975180

0.0018

0.0003

0.0022

6.3850

0.0050

0.0018

0.0068

3.6930

1980185

0.0016

0.0002

0.0018

8.0790

11

11

1980185

0.0018

0.0005

0.0022

4.8700

0.0050

0.0019

0.0069

3.7110

1985190

0.0013

0.0003

0.0017

5.4060

11

11

1985190

0.0015

0.0005

0.0020

4.1780

0.0057

0.0016

0.0072

4.6310

1990195

0.0012

0.0003

0.0016

4.6380

11

11

1990195

0.0013

0.0004

0.0017

4.7410

0.0017

0.0012

0.0029

2.4460

1995100

0.0013

0.0002

0.0015

7.9450

11

11

1995100

0.0014

0.0006

0.0020

3.4410

0.0028

0.0014

0.0042

3.0200

2000105

0.0008

0.0002

0.0009

6.2400

11

11

2000105

0.0006

0.0009

0.0014

1.6660

0.0040

0.0014

0.0054

3.8750

2005110

0.0007

0.0001

0.0009

7.5620

11

11

2005110

0.0015

0.0009

0.0024

2.6880

0.0046

0.0009

0.0055

5.9920

193512010

0.0012

0.0003

0.0015

5.3970

11

11

193512010

0.0016

0.0007

0.0023

3.2970

0.0030

0.0010

0.0040

3.8530

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!B!

!!

!!

!!

!Pane

l!D!

!!

!!

!!

!193516/68

0.0015

0.0019

0.0034

1.8190

0.0056

0.0066

0.0121

1.8500

193516/68

0.0018

0.0040

0.0058

1.4630

0.0055

0.0069

0.0123

1.7960

1935145

0.0017

0.0025

0.0043

1.6740

0.0051

0.0069

0.0119

1.7400

1935145

0.0025

0.0071

0.0096

1.3600

0.0051

0.0076

0.0127

1.6680

1946155

0.0006

0.0010

0.0016

1.5740

0.0041

0.0029

0.0070

2.4290

1946155

0.0005

0.0018

0.0023

1.2550

0.0037

0.0030

0.0067

2.2040

195616/68

0.0021

0.0020

0.0041

2.0760

0.0072

0.0092

0.0164

1.7800

195616/68

0.0024

0.0031

0.0055

1.7890

0.0073

0.0093

0.0166

1.7890

1935140

0.0018

0.0034

0.0051

1.5180

0.0079

0.0090

0.0169

1.8790

1935140

0.0019

0.0102

0.0121

1.1920

0.0086

0.0106

0.0191

1.8100

1941145

0.0017

0.0016

0.0033

2.1210

0.0019

0.0044

0.0063

1.4410

1941145

0.0033

0.0034

0.0067

1.9780

0.0011

0.0041

0.0052

1.2610

1946150

0.0009

0.0012

0.0021

1.7090

0.0049

0.0030

0.0079

2.6090

1946150

0.0012

0.0021

0.0033

1.5980

0.0050

0.0032

0.0082

2.5850

1951155

0.0003

0.0008

0.0011

1.3860

0.0035

0.0028

0.0063

2.2700

1951155

10.000

30.0015

0.0012

0.8133

0.0024

0.0029

0.0053

1.8260

1956160

0.0003

0.0007

0.0010

1.4560

0.0023

0.0038

0.0061

1.6050

1956160

0.0000

0.0019

0.0020

1.0140

0.0024

0.0042

0.0067

1.5760

196116/68

0.0033

0.0028

0.0062

2.1690

0.0106

0.0129

0.0234

1.8240

196116/68

0.0040

0.0038

0.0079

2.0480

0.0107

0.0126

0.0233

1.8470

7/196812010

0.0035

0.0016

0.0051

3.2120

0.0137

0.0070

0.0207

2.9710

7/196812010

0.0048

0.0031

0.0080

2.5300

0.0153

0.0078

0.0231

2.9450

1970180

0.0073

0.0031

0.0105

3.3360

0.0226

0.0109

0.0335

3.0720

1970180

0.0107

0.0063

0.0170

2.7100

0.0250

0.0120

0.0370

3.0800

1980190

0.0051

0.0017

0.0068

4.0490

0.0200

0.0074

0.0274

3.7270

1980190

0.0058

0.0032

0.0090

2.7930

0.0222

0.0088

0.0310

3.5350

1990100

0.0019

0.0014

0.0033

2.3770

0.0103

0.0089

0.0192

2.1630

1990100

0.0025

0.0026

0.0051

1.9540

0.0118

0.0104

0.0221

2.1350

2000110

0.0009

0.0003

0.0012

3.6320

0.0066

0.0022

0.0087

4.0140

2000110

0.0011

0.0012

0.0023

1.9600

0.0081

0.0027

0.0108

4.0210

1970175

0.0076

0.0035

0.0110

3.1740

0.0227

0.0123

0.0350

2.8440

1970175

0.0104

0.0074

0.0179

2.3970

0.0230

0.0141

0.0371

2.6250

1975180

0.0082

0.0029

0.0111

3.8740

0.0255

0.0099

0.0355

3.5730

1975180

0.0115

0.0055

0.0170

3.1020

0.0285

0.0107

0.0392

3.6760

1980185

0.0059

0.0017

0.0076

4.4210

0.0187

0.0061

0.0248

4.0520

1980185

0.0053

0.0026

0.0079

3.0210

0.0189

0.0061

0.0251

4.0810

1985190

0.0041

0.0015

0.0055

3.7670

0.0201

0.0078

0.0279

3.5710

1985190

0.0058

0.0035

0.0093

2.6350

0.0238

0.0104

0.0342

3.2920

1990195

0.0021

0.0019

0.0039

2.0990

0.0083

0.0118

0.0200

1.7030

1990195

0.0031

0.0035

0.0066

1.8970

0.0109

0.0142

0.0251

1.7680

1995100

0.0018

0.0007

0.0025

3.3900

0.0122

0.0049

0.0171

3.4910

1995100

0.0018

0.0014

0.0032

2.3270

0.0123

0.0052

0.0176

3.3640

2000105

0.0008

0.0004

0.0011

2.9260

0.0057

0.0030

0.0087

2.8800

2000105

0.0004

0.0012

0.0015

1.3340

0.0068

0.0036

0.0105

2.8810

2005110

0.0010

0.0003

0.0013

4.8240

0.0066

0.0011

0.0077

7.1170

2005110

0.0018

0.0011

0.0029

2.6110

0.0083

0.0015

0.0098

6.7380

193512010

0.0026

0.0017

0.0044

2.5410

0.0101

0.0068

0.0169

2.4930

193512010

0.0035

0.0035

0.0070

1.9980

0.0109

0.0074

0.0184

2.4740

TABLE!5c:!V

alue



ortfolios!B

uilt!Usin

g!Eq

ual1W

eighted!Securities

COMPO

NEN

TS!OF!TH

E!VA

RIAN

CES!OF!TH

E

FF

FF

s2(�

0)

s2(�

0)

s2(�

0)

s2(�

1)

s2(�

1)

s2(�

1)

s2(�

0)

s2(�

0)

s2(�

0)

s2(�

1)

s2(�

1)

s2(�

1)

�j,

t

62

Perio

d! Pane

l!A!

!!

!!

!!

!Pane

l!C!

!!

!!

!!

!193516/68

11

11

11

11

193516/68

11

11

0.2183

0.3448

0.5631

1.6330

1935145

11

11

11

11

1935145

11

11

0.2104

0.2867

0.4972

1.7340

1946155

11

11

11

11

1946155

11

11

0.1916

0.1699

0.3614

2.1280

195616/68

11

11

11

11

195616/68

11

11

0.2450

0.5354

0.7804

1.4580

1935140

11

11

11

11

1935140

11

11

0.0533

0.2877

0.3409

1.1850

1941145

11

11

11

11

1941145

11

11

0.3956

0.2856

0.6812

2.3850

1946150

11

11

11

11

1946150

11

11

0.1598

0.1556

0.3154

2.0270

1951155

11

11

11

11

1951155

11

11

0.2295

0.1841

0.4136

2.2460

1956160

11

11

11

11

1956160

11

11

0.3437

0.4751

0.8188

1.7230

196116/68

11

11

11

11

196116/68

11

11

0.1800

0.5756

0.7556

1.3130

7/196812010

11

11

11

11

7/196812010

11

11

0.3908

0.4057

0.7965

1.9630

1970180

11

11

11

11

1970180

11

11

0.6683

0.4016

1.0700

2.6640

1980190

11

11

11

11

1980190

11

11

0.1888

0.4214

0.6102

1.4480

1990100

11

11

11

11

1990100

11

11

0.1206

0.3253

0.4459

1.3710

2000110

11

11

11

11

2000110

11

11

0.4434

0.5336

0.9770

1.8310

1970175

11

11

11

11

1970175

11

11

0.8098

0.4781

1.2880

2.6940

1975180

11

11

11

11

1975180

11

11

0.6576

0.3522

1.0100

2.8670

1980185

11

11

11

11

1980185

11

11

0.2309

0.4884

0.7194

1.4730

1985190

11

11

11

11

1985190

11

11

0.0959

0.3728

0.4688

1.2570

1990195

11

11

11

11

1990195

11

11

0.1444

0.1966

0.3411

1.7350

1995100

11

11

11

11

1995100

11

11

0.0805

0.4177

0.4982

1.1930

2000105

11

11

11

11

2000105

11

11

0.2154

0.4985

0.7139

1.4320

2005110

11

11

11

11

2005110

11

11

0.6159

0.5350

1.1510

2.1510

193512010

11

11

11

11

193512010

11

11

0.3171

0.3789

0.6960

1.8370

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!B!

!!

!!

!!

!Pane

l!D!

!!

!!

!!

!193516/68

0.0007

0.0012

0.0019

1.5830

11

11

193516/68

0.0005

0.0015

0.0021

1.3400

0.1331

0.4686

0.6017

1.2840

1935145

0.0006

0.0009

0.0015

1.6030

11

11

1935145

0.0003

0.0014

0.0017

1.2540

0.1106

0.4487

0.5593

1.2470

1946155

0.0004

0.0004

0.0008

1.9400

11

11

1946155

0.0002

0.0006

0.0009

1.3580

0.1220

0.2570

0.3790

1.4750

195616/68

0.0011

0.0021

0.0032

1.5100

11

11

195616/68

0.0009

0.0024

0.0034

1.3810

0.1619

0.6553

0.8172

1.2470

1935140

0.0002

0.0012

0.0014

1.1610

11

11

1935140

0.0000

0.0019

0.0019

1.0070

10.088

50.5017

0.4133

0.8237

1941145

0.0010

0.0006

0.0016

2.7860

11

11

1941145

0.0007

0.0008

0.0015

1.9980

0.3397

0.3860

0.7257

1.8800

1946150

0.0002

0.0004

0.0006

1.6650

11

11

1946150

0.0002

0.0006

0.0007

1.3420

0.1133

0.2372

0.3505

1.4780

1951155

0.0006

0.0005

0.0011

2.1750

11

11

1951155

0.0003

0.0007

0.0010

1.3840

0.1365

0.2767

0.4132

1.4930

1956160

0.0006

0.0010

0.0016

1.5730

11

11

1956160

10.000

10.0018

0.0016

0.9260

0.0935

0.7810

0.8744

1.1200

196116/68

0.0014

0.0029

0.0043

1.5020

11

11

196116/68

0.0017

0.0029

0.0045

1.5750

0.2158

0.5716

0.7874

1.3780

7/196812010

0.0023

0.0016

0.0039

2.4170

11

11

7/196812010

0.0025

0.0024

0.0049

2.0280

0.3834

0.5015

0.8849

1.7650

1970180

0.0036

0.0019

0.0056

2.8660

11

11

1970180

0.0044

0.0031

0.0075

2.3900

0.7271

0.6402

1.3670

2.1360

1980190

0.0021

0.0017

0.0038

2.2220

11

11

1980190

0.0027

0.0031

0.0058

1.8740

0.0612

0.5702

0.6314

1.1070

1990100

0.0025

0.0026

0.0051

1.9610

11

11

1990100

0.0025

0.0040

0.0065

1.6280

0.1303

0.4085

0.5388

1.3190

2000110

0.0014

0.0006

0.0020

3.1640

11

11

2000110

0.0014

0.0006

0.0020

3.1760

0.4582

0.4852

0.9434

1.9440

1970175

0.0044

0.0022

0.0066

2.9860

11

11

1970175

0.0043

0.0035

0.0077

2.2180

0.6724

0.7218

1.3940

1.9320

1975180

0.0041

0.0018

0.0059

3.2210

11

11

1975180

0.0050

0.0033

0.0082

2.5240

0.7562

0.6297

1.3860

2.2010

1980185

0.0019

0.0011

0.0031

2.6800

11

11

1980185

0.0017

0.0014

0.0031

2.2480

0.0092

0.5573

0.5665

1.0170

1985190

0.0020

0.0021

0.0041

1.9680

11

11

1985190

0.0034

0.0044

0.0078

1.7790

0.0551

0.5845

0.6396

1.0940

1990195

0.0023

0.0035

0.0057

1.6570

11

11

1990195

0.0023

0.0059

0.0082

1.3910

0.1718

0.3511

0.5229

1.4890

1995100

0.0026

0.0014

0.0040

2.8320

11

11

1995100

0.0026

0.0015

0.0041

2.7240

0.0745

0.4143

0.4888

1.1800

2000105

0.0022

0.0010

0.0032

3.1910

11

11

2000105

0.0022

0.0010

0.0032

3.1870

0.2205

0.4580

0.6786

1.4810

2005110

0.0004

0.0002

0.0006

2.9840

11

11

2005110

0.0004

0.0002

0.0006

3.0630

0.6393

0.4859

1.1250

2.3160

193512010

0.0016

0.0014

0.0030

2.1010

11

11

193512010

0.0016

0.0020

0.0036

1.7980

0.2775

0.4870

0.7645

1.5700

FF

FF

TABLE!5c:!V

alue



ortfolios!B

uilt!Usin

g!Eq

ual1W

eighted!Securities

COMPO

NEN

TS!OF!TH

E!VA

RIAN

CES!OF!TH

E!!!!!!!!!!!!!(con

t.)

s2(�

2)

s2(�

2)

s2(�

2)

s2(�

3)

s2(�

3)

s2(�

3)

s2(�

2)

s2(�

2)

s2(�

2)

s2(�

3)

s2(�

3)

s2(�

3)

�j,

t

63

!!

!!

!!

!

Period

Period

!!

!!

!!

!!

!Pane

l!A!

!!

!!

!!

!Pane

l!C!

!!

!!

!!

!193516/68

0.0016

0.0012

0.0028

2.2660

0.0015

0.0007

0.0022

3.0780

193516/68

0.0018

0.0016

0.0034

2.0880

0.0014

0.0016

0.0030

1.8220

1935145

0.0031

0.0023

0.0053

2.3560

0.0024

0.0010

0.0034

3.3670

1935145

0.0034

0.0027

0.0061

2.2390

0.0018

0.0021

0.0039

1.8250

1946155

0.0008

0.0007

0.0014

2.1280

0.0012

0.0004

0.0016

3.9150

1946155

0.0008

0.0008

0.0016

2.0360

0.0014

0.0012

0.0027

2.1430

195616/68

0.0009

0.0008

0.0017

2.1460

0.0010

0.0007

0.0017

2.3060

195616/68

0.0012

0.0014

0.0026

1.8560

0.0009

0.0015

0.0025

1.6100

1935140

0.0051

0.0030

0.0081

2.6740

0.0032

0.0014

0.0046

3.3220

1935140

0.0055

0.0036

0.0091

2.5200

0.0021

0.0026

0.0048

1.7940

1941145

0.0008

0.0014

0.0021

1.5720

0.0015

0.0006

0.0021

3.5170

1941145

0.0010

0.0017

0.0027

1.5880

0.0014

0.0016

0.0029

1.8960

1946150

0.0013

0.0006

0.0020

3.0830

0.0017

0.0003

0.0021

6.3310

1946150

0.0012

0.0007

0.0019

2.7770

0.0020

0.0012

0.0032

2.7240

1951155

0.0001

0.0007

0.0008

1.1770

0.0006

0.0005

0.0011

2.3050

1951155

0.0003

0.0008

0.0011

1.3600

0.0008

0.0013

0.0021

1.6460

1956160

0.0000

0.0007

0.0007

1.0320

0.0004

0.0007

0.0010

1.5530

1956160

10.000

20.0013

0.0011

0.8708

0.0008

0.0018

0.0026

1.4690

196116/68

0.0015

0.0009

0.0024

2.7310

0.0013

0.0008

0.0021

2.7430

196116/68

0.0021

0.0015

0.0036

2.4310

0.0010

0.0014

0.0024

1.7490

7/196812010

0.0009

0.0011

0.0020

1.7920

0.0020

0.0010

0.0030

3.0270

7/196812010

0.0011

0.0018

0.0029

1.5920

0.0012

0.0028

0.0041

1.4260

1970180

0.0013

0.0015

0.0028

1.8410

0.0019

0.0011

0.0030

2.7680

1970180

0.0021

0.0020

0.0041

2.0650

0.0008

0.0039

0.0047

1.2170

1980190

0.0009

0.0014

0.0023

1.6040

0.0028

0.0013

0.0041

3.2130

1980190

0.0008

0.0018

0.0026

1.4310

0.0020

0.0037

0.0057

1.5470

1990100

0.0003

0.0011

0.0014

1.2840

0.0016

0.0011

0.0028

2.4470

1990100

0.0006

0.0017

0.0023

1.3540

0.0010

0.0021

0.0031

1.4840

2000110

0.0007

0.0006

0.0013

2.2220

0.0018

0.0006

0.0024

4.1700

2000110

0.0003

0.0018

0.0021

1.1750

0.0011

0.0020

0.0031

1.5530

1970175

0.0021

0.0018

0.0039

2.1500

0.0015

0.0012

0.0027

2.1830

1970175

0.0030

0.0025

0.0055

2.2300

0.0013

0.0042

0.0055

1.3140

1975180

0.0009

0.0014

0.0023

1.6560

0.0022

0.0010

0.0032

3.0880

1975180

0.0021

0.0017

0.0039

2.2290

0.0008

0.0040

0.0048

1.1960

1980185

0.0010

0.0013

0.0024

1.7960

0.0024

0.0011

0.0035

3.2000

1980185

0.0009

0.0015

0.0025

1.5830

0.0027

0.0038

0.0065

1.7030

1985190

0.0006

0.0015

0.0021

1.4300

0.0029

0.0013

0.0042

3.1430

1985190

0.0006

0.0019

0.0025

1.3140

0.0013

0.0032

0.0045

1.3900

1990195

0.0000

0.0012

0.0012

0.9897

0.0013

0.0012

0.0024

2.0710

1990195

0.0001

0.0015

0.0016

1.0910

0.0002

0.0021

0.0023

1.0820

1995100

0.0008

0.0009

0.0017

1.9360

0.0020

0.0010

0.0030

3.0890

1995100

0.0013

0.0018

0.0030

1.7070

0.0019

0.0018

0.0037

2.0580

2000105

0.0004

0.0006

0.0010

1.7480

0.0014

0.0007

0.0021

2.9550

2000105

10.000

10.0014

0.0014

0.9591

0.0008

0.0019

0.0027

1.4340

2005110

0.0008

0.0005

0.0013

2.6920

0.0020

0.0004

0.0024

6.4460

2005110

0.0006

0.0020

0.0026

1.2880

0.0010

0.0020

0.0030

1.5150

193512010

0.0012

0.0012

0.0024

2.0080

0.0018

0.0009

0.0026

3.0450

193512010

0.0014

0.0017

0.0031

1.7970

0.0013

0.0023

0.0036

1.5550

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!B!

!!

!!

!!

!Pane

l!D!

!!

!!

!!

!193516/68

10.000

10.0066

0.0065

0.9895

0.0025

0.0217

0.0242

1.1170

193516/68

0.0000

0.0092

0.0092

0.9985

0.0024

0.0235

0.0259

1.1010

1935145

0.0003

0.0086

0.0088

1.0290

0.0027

0.0212

0.0239

1.1270

1935145

0.0016

0.0121

0.0138

1.1340

0.0044

0.0231

0.0275

1.1910

1946155

10.000

40.0046

0.0042

0.9159

0.0021

0.0134

0.0156

1.1570

1946155

10.000

60.0054

0.0048

0.8826

0.0016

0.0133

0.0148

1.1180

195616/68

0.0000

0.0064

0.0064

0.9977

0.0030

0.0287

0.0318

1.1060

195616/68

10.000

80.0096

0.0088

0.9137

0.0016

0.0321

0.0336

1.0490

1935140

0.0026

0.0097

0.0123

1.2690

0.0089

0.0225

0.0314

1.3970

1935140

0.0068

0.0129

0.0197

1.5250

0.0142

0.0238

0.0380

1.5960

1941145

10.002

40.0073

0.0049

0.6695

10.004

40.0197

0.0154

0.7793

1941145

10.004

30.0112

0.0069

0.6187

10.006

80.0222

0.0154

0.6958

1946150

10.000

50.0043

0.0037

0.8779

0.0007

0.0096

0.0104

1.0770

1946150

10.000

30.0048

0.0045

0.9466

0.0003

0.0095

0.0098

1.0370

1951155

10.000

20.0049

0.0047

0.9594

0.0037

0.0172

0.0210

1.2160

1951155

10.001

00.0061

0.0051

0.8289

0.0030

0.0170

0.0201

1.1790

1956160

10.000

20.0035

0.0033

0.9399

0.0013

0.0200

0.0213

1.0670

1956160

10.000

60.0043

0.0037

0.8617

0.0008

0.0202

0.0210

1.0400

196116/68

0.0001

0.0084

0.0085

1.0170

0.0042

0.0346

0.0388

1.1210

196116/68

10.000

90.0132

0.0122

0.9294

0.0020

0.0400

0.0420

1.0510

7/196812010

0.0018

0.0074

0.0092

1.2380

0.0062

0.0307

0.0369

1.2030

7/196812010

0.0023

0.0090

0.0113

1.2580

0.0043

0.0333

0.0376

1.1310

1970180

0.0080

0.0147

0.0226

1.5420

0.0248

0.0471

0.0720

1.5270

1970180

0.0109

0.0159

0.0268

1.6850

0.0191

0.0497

0.0688

1.3830

1980190

0.0003

0.0080

0.0083

1.0370

0.0058

0.0330

0.0388

1.1760

1980190

10.000

30.0102

0.0100

0.9731

0.0051

0.0373

0.0424

1.1370

1990100

10.001

70.0051

0.0033

0.6588

10.009

30.0345

0.0251

0.7292

1990100

10.002

00.0072

0.0052

0.7175

10.009

30.0378

0.0285

0.7528

2000110

0.0002

0.0015

0.0017

1.1440

0.0014

0.0093

0.0107

1.1550

2000110

0.0000

0.0025

0.0025

0.9953

0.0007

0.0120

0.0127

1.0610

1970175

0.0102

0.0176

0.0278

1.5800

0.0273

0.0560

0.0833

1.4870

1970175

0.0142

0.0190

0.0332

1.7430

0.0244

0.0593

0.0837

1.4100

1975180

0.0063

0.0121

0.0183

1.5190

0.0220

0.0395

0.0615

1.5580

1975180

0.0083

0.0129

0.0212

1.6440

0.0123

0.0429

0.0551

1.2860

1980185

0.0018

0.0085

0.0103

1.2160

0.0118

0.0300

0.0419

1.3930

1980185

0.0021

0.0101

0.0122

1.2080

0.0100

0.0320

0.0420

1.3130

1985190

10.000

50.0069

0.0064

0.9281

0.0043

0.0334

0.0377

1.1270

1985190

10.001

00.0096

0.0085

0.8926

0.0043

0.0393

0.0436

1.1090

1990195

10.002

30.0062

0.0039

0.6320

10.013

40.0398

0.0264

0.6627

1990195

10.002

80.0088

0.0060

0.6800

10.013

20.0453

0.0321

0.7086

1995100

10.000

60.0034

0.0028

0.8181

10.002

30.0248

0.0225

0.9057

1995100

10.000

40.0047

0.0043

0.9048

10.002

40.0255

0.0231

0.9072

2000105

10.000

10.0017

0.0016

0.9610

10.002

60.0131

0.0105

0.8024

2000105

10.000

50.0024

0.0019

0.7810

10.002

60.0149

0.0122

0.8230

2005110

0.0005

0.0012

0.0017

1.4530

0.0049

0.0044

0.0092

2.1130

2005110

0.0004

0.0024

0.0029

1.1800

0.0037

0.0080

0.0117

1.4670

193512010

0.0010

0.0071

0.0080

1.1350

0.0046

0.0267

0.0313

1.1710

193512010

0.0013

0.0091

0.0103

1.1410

0.0035

0.0290

0.0324

1.1190

TABLE!5d

:!Value



ortfolios!Bu

ilt!Using!Value

1Weighted!Securitie

sCO

MPO

NEN

TS!OF!TH

E!VARIANCE

S!OF!TH

E

FF

FF

s2(�

0)

s2(�

0)

s2(�

0)

s2(�

1)

s2(�

1)

s2(�

1)

s2(�

0)

s2(�

0)

s2(�

0)

s2(�

1)

s2(�

1)

s2(�

1)

�j,

t

64

Period

! Pane

l!A!

!!

!!

!!

!Pane

l!C!

!!

!!

!!

!193516/68

11

11

11

11

193516/68

11

11

0.1638

0.4877

0.6515

1.3360

1935145

11

11

11

11

1935145

11

11

10.048

10.2734

0.2252

0.8239

1946155

11

11

11

11

1946155

11

11

0.2441

0.4152

0.6593

1.5880

195616/68

11

11

11

11

195616/68

11

11

0.2895

0.7330

1.0230

1.3950

1935140

11

11

11

11

1935140

11

11

10.011

20.2109

0.1997

0.9470

1941145

11

11

11

11

1941145

11

11

10.088

60.3473

0.2587

0.7450

1946150

11

11

11

11

1946150

11

11

0.2113

0.3070

0.5183

1.6880

1951155

11

11

11

11

1951155

11

11

0.2834

0.5234

0.8069

1.5420

1956160

11

11

11

11

1956160

11

11

0.7421

0.9252

1.6670

1.8020

196116/68

11

11

11

11

196116/68

11

11

0.0005

0.6048

0.6053

1.0010

7/196812010

11

11

11

11

7/196812010

11

11

0.0282

0.7707

0.7989

1.0370

1970180

11

11

11

11

1970180

11

11

0.3510

1.0530

1.4040

1.3330

1980190

11

11

11

11

1980190

11

11

10.134

00.6760

0.5421

0.8018

1990100

11

11

11

11

1990100

11

11

0.0157

0.4121

0.4277

1.0380

2000110

11

11

11

11

2000110

11

11

10.229

30.8347

0.6054

0.7253

1970175

11

11

11

11

1970175

11

11

0.4023

1.3880

1.7900

1.2900

1975180

11

11

11

11

1975180

11

11

0.4290

0.8960

1.3250

1.4790

1980185

11

11

11

11

1980185

11

11

10.030

30.6855

0.6553

0.9559

1985190

11

11

11

11

1985190

11

11

10.204

80.6287

0.4239

0.6743

1990195

11

11

11

11

1990195

11

11

10.033

90.3200

0.2861

0.8939

1995100

11

11

11

11

1995100

11

11

0.0697

0.4624

0.5321

1.1510

2000105

11

11

11

11

2000105

11

11

10.067

40.5495

0.4821

0.8773

2005110

11

11

11

11

2005110

11

11

10.452

71.0950

0.6427

0.5867

193512010

11

11

11

11

193512010

11

11

0.0906

0.6461

0.7367

1.1400

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!B!

!!

!!

!!

!Pane

l!D!

!!

!!

!!

!193516/68

0.0003

0.0041

0.0044

1.0750

11

11

193516/68

0.0000

0.0047

0.0048

1.0070

0.1242

0.5770

0.7012

1.2150

1935145

10.000

10.0027

0.0027

0.9790

11

11

1935145

0.0000

0.0034

0.0035

1.0130

10.027

30.3705

0.3431

0.9263

1946155

0.0003

0.0022

0.0025

1.1290

11

11

1946155

0.0000

0.0024

0.0024

1.0110

0.2124

0.4713

0.6837

1.4510

195616/68

0.0007

0.0067

0.0074

1.0990

11

11

195616/68

0.0001

0.0078

0.0078

1.0070

0.1937

0.8421

1.0360

1.2300

1935140

0.0003

0.0028

0.0031

1.0970

11

11

1935140

0.0009

0.0035

0.0043

1.2460

0.0735

0.3031

0.3766

1.2430

1941145

10.000

40.0026

0.0022

0.8417

11

11

1941145

10.000

90.0034

0.0025

0.7442

10.141

80.4502

0.3085

0.6851

1946150

0.0001

0.0011

0.0012

1.0560

11

11

1946150

0.0000

0.0012

0.0013

1.0360

0.2342

0.3440

0.5782

1.6810

1951155

0.0005

0.0032

0.0038

1.1640

11

11

1951155

0.0000

0.0035

0.0036

1.0140

0.1956

0.5985

0.7941

1.3270

1956160

10.000

40.0056

0.0052

0.9254

11

11

1956160

10.000

70.0055

0.0049

0.8822

0.6839

0.9556

1.6390

1.7160

196116/68

0.0013

0.0075

0.0088

1.1740

11

11

196116/68

0.0005

0.0092

0.0097

1.0490

10.121

50.7664

0.6449

0.8415

7/196812010

0.0006

0.0069

0.0076

1.0880

11

11

7/196812010

0.0006

0.0078

0.0084

1.0760

0.0024

0.8456

0.8480

1.0030

1970180

0.0033

0.0080

0.0113

1.4110

11

11

1970180

0.0037

0.0084

0.0121

1.4470

0.3277

1.1210

1.4490

1.2920

1980190

0.0006

0.0074

0.0080

1.0780

11

11

1980190

0.0005

0.0096

0.0101

1.0490

10.152

50.7828

0.6303

0.8052

1990100

10.002

30.0108

0.0085

0.7870

11

11

1990100

10.002

70.0128

0.0100

0.7850

10.021

30.4797

0.4583

0.9555

2000110

10.000

30.0029

0.0027

0.9136

11

11

2000110

10.000

20.0029

0.0027

0.9248

10.240

50.9174

0.6769

0.7378

1970175

0.0048

0.0093

0.0141

1.5180

11

11

1970175

0.0055

0.0096

0.0151

1.5770

0.3866

1.4470

1.8330

1.2670

1975180

0.0020

0.0069

0.0089

1.2910

11

11

1975180

0.0020

0.0074

0.0094

1.2710

0.3683

0.9723

1.3410

1.3790

1980185

0.0019

0.0057

0.0077

1.3410

11

11

1980185

0.0021

0.0066

0.0086

1.3140

10.020

20.7784

0.7581

0.9740

1985190

0.0002

0.0085

0.0088

1.0270

11

11

1985190

0.0002

0.0117

0.0119

1.0180

10.220

40.7245

0.5042

0.6958

1990195

10.003

20.0121

0.0089

0.7330

11

11

1990195

10.003

90.0158

0.0119

0.7546

10.066

40.4250

0.3587

0.8439

1995100

10.000

80.0080

0.0072

0.9032

11

11

1995100

10.000

90.0081

0.0072

0.8918

0.0374

0.4822

0.5197

1.0780

2000105

10.000

80.0046

0.0038

0.8213

11

11

2000105

10.000

70.0046

0.0039

0.8406

10.035

50.5769

0.5415

0.9385

2005110

0.0001

0.0008

0.0009

1.1340

11

11

2005110

0.0001

0.0009

0.0010

1.1220

10.506

71.2390

0.7326

0.5912

193512010

0.0005

0.0057

0.0061

1.0830

11

11

193512010

0.0003

0.0065

0.0068

1.0530

0.0589

0.7274

0.7863

1.0810

FF

FF

TABLE!5d

:!Value



ortfolios!Bu

ilt!Using!Value

1Weighted!Securitie

sCO

MPO

NEN

TS!OF!TH

E!VARIANCE

S!OF!TH

E!!!!!!!!!!!!!(con

t.)

s2(�

2)

s2(�

2)

s2(�

2)

s2(�

3)

s2(�

3)

s2(�

3)

s2(�

2)

s2(�

2)

s2(�

2)

s2(�

3)

s2(�

3)

s2(�

3)

�j,

t

65

!!

!!

!!

!

Period

Period

!!

!!

!!

!!

!Pane

l!A!

!!

!!

!!

!Pane

l!C!

!!

!!

!!

!193516/68

0.0012

0.0008

0.0020

2.4090

0.0022

0.0008

0.0030

3.8820

193516/68

0.0012

0.0010

0.0022

2.2610

0.0022

0.0020

0.0042

2.1080

1935145

0.0022

0.0015

0.0037

2.4200

0.0040

0.0014

0.0054

3.9350

1935145

0.0022

0.0017

0.0039

2.2660

0.0032

0.0038

0.0070

1.8290

1946155

0.0007

0.0005

0.0012

2.5880

0.0015

0.0004

0.0019

4.5960

1946155

0.0009

0.0005

0.0014

2.8190

0.0022

0.0010

0.0031

3.2350

195616/68

0.0007

0.0006

0.0013

2.3090

0.0012

0.0005

0.0017

3.3400

195616/68

0.0007

0.0007

0.0014

1.9680

0.0014

0.0012

0.0026

2.1750

1935140

0.0037

0.0019

0.0056

2.9030

0.0059

0.0018

0.0077

4.3060

1935140

0.0037

0.0021

0.0058

2.7750

0.0043

0.0048

0.0091

1.8820

1941145

0.0005

0.0011

0.0015

1.4250

0.0019

0.0009

0.0028

3.0630

1941145

0.0004

0.0013

0.0017

1.3410

0.0019

0.0026

0.0045

1.7400

1946150

0.0011

0.0004

0.0015

3.8380

0.0019

0.0003

0.0023

6.4550

1946150

0.0012

0.0004

0.0016

3.8700

0.0029

0.0010

0.0040

3.8440

1951155

0.0003

0.0005

0.0008

1.6330

0.0010

0.0005

0.0015

3.2540

1951155

0.0006

0.0006

0.0012

2.0690

0.0014

0.0009

0.0023

2.5830

1956160

0.0003

0.0005

0.0008

1.5750

0.0005

0.0005

0.0010

2.1960

1956160

0.0004

0.0008

0.0011

1.4630

0.0006

0.0009

0.0015

1.6240

196116/68

0.0010

0.0006

0.0015

2.6780

0.0016

0.0006

0.0021

3.8120

196116/68

0.0009

0.0007

0.0016

2.3170

0.0019

0.0014

0.0033

2.3400

7/196812010

0.0006

0.0008

0.0014

1.8270

0.0022

0.0008

0.0030

3.6740

7/196812010

0.0009

0.0011

0.0020

1.8680

0.0018

0.0027

0.0045

1.6640

1970180

0.0013

0.0008

0.0020

2.6410

0.0034

0.0008

0.0042

5.1030

1970180

0.0017

0.0012

0.0029

2.3490

0.0007

0.0040

0.0047

1.1780

1980190

0.0006

0.0010

0.0016

1.5530

0.0021

0.0011

0.0032

2.8860

1980190

0.0009

0.0013

0.0021

1.6670

0.0031

0.0033

0.0064

1.9330

1990100

0.0003

0.0009

0.0012

1.3750

0.0013

0.0009

0.0022

2.4770

1990100

0.0007

0.0010

0.0017

1.6900

0.0013

0.0017

0.0031

1.7710

2000110

0.0004

0.0006

0.0010

1.6730

0.0020

0.0006

0.0026

4.6260

2000110

0.0007

0.0009

0.0016

1.8330

0.0024

0.0019

0.0042

2.2690

1970175

0.0018

0.0008

0.0026

3.1770

0.0034

0.0008

0.0043

5.1210

1970175

0.0023

0.0014

0.0038

2.6120

0.0002

0.0051

0.0053

1.0490

1975180

0.0007

0.0008

0.0016

1.9270

0.0038

0.0009

0.0047

5.3240

1975180

0.0012

0.0013

0.0024

1.9380

0.0011

0.0033

0.0045

1.3410

1980185

0.0009

0.0007

0.0016

2.2720

0.0020

0.0008

0.0028

3.6540

1980185

0.0010

0.0009

0.0019

2.0790

0.0023

0.0026

0.0049

1.8920

1985190

0.0002

0.0013

0.0015

1.1930

0.0020

0.0013

0.0033

2.5210

1985190

0.0006

0.0015

0.0022

1.4000

0.0034

0.0039

0.0073

1.8880

1990195

0.0000

0.0011

0.0010

0.9634

0.0011

0.0011

0.0022

2.0120

1990195

0.0002

0.0012

0.0014

1.1830

0.0011

0.0018

0.0029

1.6430

1995100

0.0008

0.0006

0.0014

2.2690

0.0015

0.0006

0.0021

3.5730

1995100

0.0012

0.0007

0.0020

2.7170

0.0014

0.0015

0.0029

1.9250

2000105

0.0004

0.0006

0.0011

1.7200

0.0014

0.0006

0.0020

3.2690

2000105

0.0009

0.0009

0.0018

1.9700

0.0007

0.0017

0.0024

1.4270

2005110

0.0003

0.0005

0.0007

1.5510

0.0025

0.0005

0.0029

6.3980

2005110

0.0005

0.0008

0.0013

1.6440

0.0036

0.0019

0.0055

2.9270

193512010

0.0009

0.0008

0.0017

2.0920

0.0022

0.0008

0.0030

3.7610

193512010

0.0011

0.0010

0.0021

2.0310

0.0020

0.0024

0.0044

1.8250

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!B!

!!

!!

!!

!Pane

l!D!

!!

!!

!!

!193516/68

0.0004

0.0041

0.0045

1.0990

0.0070

0.0181

0.0251

1.3890

193516/68

0.0005

0.0051

0.0056

1.1000

0.0057

0.0183

0.0240

1.3100

1935145

10.000

80.0054

0.0047

0.8619

0.0081

0.0258

0.0339

1.3140

1935145

0.0005

0.0070

0.0075

1.0660

0.0081

0.0263

0.0344

1.3080

1946155

0.0018

0.0028

0.0046

1.6340

0.0114

0.0112

0.0226

2.0150

1946155

0.0007

0.0036

0.0042

1.1830

0.0078

0.0114

0.0192

1.6870

195616/68

0.0004

0.0039

0.0043

1.0920

0.0029

0.0168

0.0197

1.1730

195616/68

0.0005

0.0045

0.0050

1.1020

0.0020

0.0169

0.0190

1.1210

1935140

10.001

20.0068

0.0056

0.8225

0.0139

0.0323

0.0463

1.4300

1935140

10.000

50.0084

0.0079

0.9350

0.0124

0.0330

0.0454

1.3750

1941145

10.000

30.0038

0.0035

0.9309

0.0014

0.0181

0.0195

1.0780

1941145

0.0017

0.0053

0.0070

1.3100

0.0033

0.0183

0.0216

1.1790

1946150

0.0009

0.0018

0.0027

1.4990

0.0069

0.0068

0.0137

2.0110

1946150

0.0003

0.0024

0.0027

1.1250

0.0062

0.0068

0.0130

1.9060

1951155

0.0028

0.0039

0.0066

1.7160

0.0160

0.0156

0.0316

2.0260

1951155

0.0011

0.0048

0.0059

1.2260

0.0096

0.0159

0.0255

1.6020

1956160

10.000

20.0024

0.0022

0.9071

0.0013

0.0107

0.0120

1.1190

1956160

10.000

30.0029

0.0026

0.8831

10.000

30.0111

0.0108

0.9720

196116/68

0.0008

0.0050

0.0057

1.1540

0.0042

0.0208

0.0250

1.2000

196116/68

0.0010

0.0056

0.0066

1.1830

0.0037

0.0208

0.0246

1.1800

7/196812010

0.0012

0.0039

0.0051

1.2990

0.0105

0.0203

0.0307

1.5160

7/196812010

0.0019

0.0048

0.0067

1.4040

0.0109

0.0213

0.0322

1.5100

1970180

0.0036

0.0064

0.0100

1.5630

0.0215

0.0299

0.0514

1.7190

1970180

0.0048

0.0078

0.0126

1.6220

0.0215

0.0321

0.0536

1.6680

1980190

0.0021

0.0050

0.0071

1.4150

0.0153

0.0254

0.0406

1.6020

1980190

0.0037

0.0063

0.0100

1.5900

0.0150

0.0263

0.0413

1.5720

1990100

10.000

20.0030

0.0027

0.9214

0.0033

0.0193

0.0226

1.1710

1990100

0.0005

0.0035

0.0040

1.1320

0.0053

0.0187

0.0240

1.2850

2000110

10.000

20.0015

0.0013

0.8830

0.0075

0.0085

0.0160

1.8850

2000110

10.000

10.0018

0.0016

0.9282

0.0091

0.0095

0.0185

1.9570

1970175

0.0020

0.0062

0.0082

1.3150

0.0081

0.0288

0.0369

1.2820

1970175

0.0026

0.0082

0.0108

1.3210

0.0167

0.0314

0.0481

1.5310

1975180

0.0072

0.0068

0.0139

2.0610

0.0387

0.0322

0.0708

2.2020

1975180

0.0086

0.0074

0.0160

2.1500

0.0361

0.0348

0.0709

2.0350

1980185

0.0027

0.0049

0.0076

1.5460

0.0165

0.0227

0.0392

1.7270

1980185

0.0032

0.0060

0.0093

1.5370

0.0171

0.0232

0.0403

1.7370

1985190

0.0018

0.0046

0.0063

1.3870

0.0145

0.0250

0.0395

1.5780

1985190

0.0046

0.0059

0.0105

1.7890

0.0138

0.0264

0.0402

1.5210

1990195

10.000

90.0043

0.0034

0.7988

0.0011

0.0291

0.0303

1.0380

1990195

10.000

30.0048

0.0045

0.9352

0.0022

0.0283

0.0305

1.0790

1995100

0.0006

0.0013

0.0018

1.4330

0.0053

0.0069

0.0123

1.7700

1995100

0.0015

0.0019

0.0034

1.7670

0.0081

0.0068

0.0149

2.1980

2000105

10.000

30.0016

0.0013

0.8201

0.0035

0.0093

0.0128

1.3800

2000105

10.000

10.0019

0.0018

0.9470

0.0043

0.0097

0.0140

1.4410

2005110

10.000

10.0012

0.0012

0.9541

0.0103

0.0071

0.0174

2.4390

2005110

10.000

10.0015

0.0014

0.9496

0.0116

0.0087

0.0203

2.3420

193512010

0.0008

0.0040

0.0048

1.2110

0.0090

0.0193

0.0283

1.4660

193512010

0.0013

0.0049

0.0062

1.2670

0.0086

0.0200

0.0286

1.4300

TABLE!5f:!Equ

al1W


rtfolio!!!!!!!!!+!!!!!!!5x5!Dou

ble1Sort!Test!Po

rtfolios!Bu

ilt!Using!Value


COMPO

NEN

TS!OF!TH

E!VARIANCE

S!OF!TH

E

FF

FF

s2(�

0)

s2(�

0)

s2(�

0)

s2(�

1)

s2(�

1)

s2(�

1)

s2(�

0)

s2(�

0)

s2(�

0)

s2(�

1)

s2(�

1)

s2(�

1)

�j,

t

66

Period

! Pane

l!A!

!!

!!

!!

!Pane

l!C!

!!

!!

!!

!193516/68

11

11

11

11

193516/68

11

11

0.1763

0.2919

0.4682

1.6040

1935145

11

11

11

11

1935145

11

11

0.0485

0.2344

0.2829

1.2070

1946155

11

11

11

11

1946155

11

11

0.2446

0.2233

0.4679

2.0960

195616/68

11

11

11

11

195616/68

11

11

0.2302

0.3971

0.6273

1.5800

1935140

11

11

11

11

1935140

11

11

0.0921

0.1785

0.2706

1.5160

1941145

11

11

11

11

1941145

11

11

0.0015

0.3006

0.3021

1.0050

1946150

11

11

11

11

1946150

11

11

0.2626

0.1734

0.4360

2.5150

1951155

11

11

11

11

1951155

11

11

0.2325

0.2732

0.5057

1.8510

1956160

11

11

11

11

1956160

11

11

0.1277

0.4014

0.5290

1.3180

196116/68

11

11

11

11

196116/68

11

11

0.3024

0.3942

0.6966

1.7670

7/196812010

11

11

11

11

7/196812010

11

11

0.2370

0.5695

0.8065

1.4160

1970180

11

11

11

11

1970180

11

11

0.2008

0.9615

1.1620

1.2090

1980190

11

11

11

11

1980190

11

11

0.3509

0.5776

0.9285

1.6080

1990100

11

11

11

11

1990100

11

11

0.2565

0.2631

0.5195

1.9750

2000110

11

11

11

11

2000110

11

11

0.3076

0.4434

0.7510

1.6940

1970175

11

11

11

11

1970175

11

11

0.1047

1.3510

1.4560

1.0770

1975180

11

11

11

11

1975180

11

11

0.1168

0.7044

0.8212

1.1660

1980185

11

11

11

11

1980185

11

11

0.1212

0.4626

0.5838

1.2620

1985190

11

11

11

11

1985190

11

11

0.4937

0.6875

1.1810

1.7180

1990195

11

11

11

11

1990195

11

11

0.2240

0.2397

0.4637

1.9340

1995100

11

11

11

11

1995100

11

11

0.2701

0.2640

0.5341

2.0230

2000105

11

11

11

11

2000105

11

11

0.3632

0.3586

0.7217

2.0130

2005110

11

11

11

11

2005110

11

11

0.2401

0.4928

0.7328

1.4870

193512010

11

11

11

11

193512010

11

11

0.2097

0.4473

0.6570

1.4690

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!B!

!!

!!

!!

!Pane

l!D!

!!

!!

!!

!193516/68

0.0009

0.0040

0.0049

1.2160

11

11

193516/68

0.0008

0.0047

0.0054

1.1710

0.1660

0.3376

0.5035

1.4920

1935145

0.0008

0.0061

0.0069

1.1300

11

11

1935145

0.0018

0.0075

0.0093

1.2460

0.1008

0.2957

0.3965

1.3410

1946155

0.0021

0.0023

0.0043

1.9280

11

11

1946155

0.0010

0.0025

0.0035

1.4000

0.1644

0.2668

0.4313

1.6160

195616/68

0.0000

0.0036

0.0037

1.0050

11

11

195616/68

10.000

30.0039

0.0036

0.9350

0.2195

0.4307

0.6502

1.5100

1935140

0.0014

0.0077

0.0091

1.1810

11

11

1935140

0.0016

0.0096

0.0112

1.1670

0.0927

0.2408

0.3335

1.3850

1941145

0.0000

0.0042

0.0041

0.9940

11

11

1941145

0.0021

0.0050

0.0071

1.4200

0.1172

0.3607

0.4778

1.3250

1946150

0.0008

0.0013

0.0021

1.6710

11

11

1946150

0.0005

0.0014

0.0020

1.3520

0.1729

0.2308

0.4037

1.7490

1951155

0.0034

0.0032

0.0066

2.0350

11

11

1951155

0.0015

0.0036

0.0052

1.4270

0.1631

0.3029

0.4660

1.5390

1956160

0.0004

0.0024

0.0028

1.1690

11

11

1956160

0.0001

0.0025

0.0026

1.0370

0.0660

0.4300

0.4959

1.1530

196116/68

10.000

20.0045

0.0043

0.9530

11

11

196116/68

10.000

50.0047

0.0043

0.9051

0.3248

0.4312

0.7560

1.7530

7/196812010

0.0017

0.0053

0.0070

1.3110

11

11

7/196812010

0.0020

0.0058

0.0078

1.3540

0.2949

0.6178

0.9127

1.4770

1970180

0.0040

0.0070

0.0110

1.5780

11

11

1970180

0.0048

0.0075

0.0123

1.6480

0.3180

1.0360

1.3540

1.3070

1980190

0.0032

0.0068

0.0100

1.4680

11

11

1980190

0.0040

0.0079

0.0119

1.5070

0.4838

0.6432

1.1270

1.7520

1990100

0.0005

0.0061

0.0066

1.0820

11

11

1990100

0.0007

0.0062

0.0069

1.1200

0.3100

0.3040

0.6140

2.0200

2000110

0.0008

0.0023

0.0031

1.3440

11

11

2000110

0.0005

0.0023

0.0028

1.2420

0.2464

0.4451

0.6915

1.5540

1970175

0.0021

0.0067

0.0088

1.3200

11

11

1970175

0.0036

0.0074

0.0110

1.4830

0.3078

1.4780

1.7860

1.2080

1975180

0.0083

0.0077

0.0160

2.0830

11

11

1975180

0.0091

0.0079

0.0170

2.1540

0.2186

0.6982

0.9169

1.3130

1980185

0.0035

0.0055

0.0089

1.6330

11

11

1980185

0.0036

0.0060

0.0096

1.6040

0.1699

0.4869

0.6568

1.3490

1985190

0.0030

0.0073

0.0103

1.4040

11

11

1985190

0.0047

0.0088

0.0136

1.5330

0.7328

0.7799

1.5130

1.9400

1990195

10.000

70.0095

0.0088

0.9267

11

11

1990195

10.000

40.0096

0.0092

0.9611

0.2407

0.2628

0.5035

1.9160

1995100

0.0016

0.0018

0.0035

1.8900

11

11

1995100

0.0018

0.0021

0.0039

1.8310

0.3575

0.3304

0.6879

2.0820

2000105

0.0008

0.0026

0.0034

1.3240

11

11

2000105

0.0004

0.0025

0.0029

1.1610

0.3210

0.3621

0.6831

1.8860

2005110

0.0005

0.0019

0.0024

1.2770

11

11

2005110

0.0005

0.0019

0.0024

1.2560

0.1704

0.4933

0.6638

1.3450

193512010

0.0013

0.0048

0.0061

1.2760

11

11

193512010

0.0015

0.0053

0.0068

1.2830

0.2377

0.4944

0.7322

1.4810

FF

FF

TABLE!5f:!Equ

al1W


rtfolio!!!!!!!!!+!!!!!!!5x5!Dou

ble1Sort!Test!Po

rtfolios!Bu

ilt!Using!Value


COMPO

NEN

TS!OF!TH

E!VARIANCE

S!OF!TH

E!!!!!!!!!!!!!(con

t.)

s2(�

2)

s2(�

2)

s2(�

2)

s2(�

3)

s2(�

3)

s2(�

3)

s2(�

2)

s2(�

2)

s2(�

2)

s2(�

3)

s2(�

3)

s2(�

3)

�j,

t

67

!!

!!

!!

!

Period

Period

!!

!!

!!

!!

!Pane

l!A!

!!

!!

!!

!Pane

l!C!

!!

!!

!!

!193516/68

0.0010

0.0004

0.0014

3.3720

11

11

193516/68

0.0012

0.0003

0.0015

4.4730

0.0022

0.0003

0.0026

7.5410

1935145

0.0014

0.0009

0.0023

2.4920

11

11

1935145

0.0017

0.0007

0.0025

3.3810

0.0037

0.0006

0.0043

6.8840

1946155

0.0006

0.0001

0.0007

5.4590

11

11

1946155

0.0006

0.0001

0.0008

6.6900

0.0016

0.0001

0.0017

12.3400

195616/68

0.0009

0.0002

0.0011

6.2840

11

11

195616/68

0.0011

0.0002

0.0012

7.5590

0.0015

0.0003

0.0018

6.9390

1935140

0.0018

0.0015

0.0033

2.2430

11

11

1935140

0.0023

0.0011

0.0034

3.1030

0.0056

0.0008

0.0064

7.6090

1941145

0.0009

0.0003

0.0012

3.9670

11

11

1941145

0.0011

0.0003

0.0014

4.7990

0.0015

0.0004

0.0018

5.0490

1946150

0.0009

0.0001

0.0010

8.2990

11

11

1946150

0.0008

0.0001

0.0009

8.9280

0.0021

0.0001

0.0022

15.5300

1951155

0.0002

0.0001

0.0004

2.8020

11

11

1951155

0.0004

0.0001

0.0006

4.6060

0.0011

0.0001

0.0013

9.1860

1956160

0.0002

0.0001

0.0004

2.4770

11

11

1956160

0.0004

0.0002

0.0006

3.7670

0.0011

0.0002

0.0013

7.2190

196116/68

0.0013

0.0002

0.0015

7.6980

11

11

196116/68

0.0014

0.0002

0.0015

9.2900

0.0017

0.0003

0.0021

6.6520

7/196812010

0.0013

0.0003

0.0016

5.9720

11

11

7/196812010

0.0016

0.0002

0.0018

7.5020

0.0030

0.0006

0.0036

5.8420

1970180

0.0019

0.0003

0.0022

7.3280

11

11

1970180

0.0020

0.0003

0.0023

8.5300

0.0037

0.0010

0.0047

4.5590

1980190

0.0016

0.0003

0.0019

6.3970

11

11

1980190

0.0018

0.0003

0.0020

7.4470

0.0039

0.0008

0.0047

5.7230

1990100

0.0011

0.0004

0.0015

4.2240

11

11

1990100

0.0017

0.0003

0.0020

7.0360

0.0026

0.0004

0.0031

6.8950

2000110

0.0007

0.0002

0.0009

4.7320

11

11

2000110

0.0011

0.0002

0.0013

6.0550

0.0029

0.0004

0.0032

9.2140

1970175

0.0021

0.0003

0.0024

7.8660

11

11

1970175

0.0023

0.0003

0.0026

9.7050

0.0037

0.0010

0.0047

4.7410

1975180

0.0018

0.0003

0.0022

6.4350

11

11

1975180

0.0018

0.0003

0.0021

6.9130

0.0043

0.0012

0.0055

4.5180

1980185

0.0015

0.0002

0.0018

7.3640

11

11

1980185

0.0016

0.0002

0.0018

7.7830

0.0034

0.0009

0.0043

4.8200

1985190

0.0016

0.0003

0.0019

5.9930

11

11

1985190

0.0019

0.0003

0.0022

7.4640

0.0041

0.0007

0.0048

6.9150

1990195

0.0010

0.0004

0.0015

3.4800

11

11

1990195

0.0015

0.0003

0.0018

5.4960

0.0019

0.0005

0.0024

4.5450

1995100

0.0012

0.0003

0.0015

5.9000

11

11

1995100

0.0019

0.0002

0.0021

9.9920

0.0031

0.0003

0.0034

11.2200

2000105

0.0007

0.0002

0.0009

4.4120

11

11

2000105

0.0013

0.0002

0.0015

7.0050

0.0024

0.0003

0.0028

7.9820

2005110

0.0006

0.0002

0.0008

4.9680

11

11

2005110

0.0008

0.0002

0.0010

4.9120

0.0029

0.0003

0.0033

10.1600

193512010

0.0012

0.0003

0.0015

4.5390

11

11

193512010

0.0014

0.0003

0.0017

5.9260

0.0027

0.0005

0.0032

6.3490

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!B!

!!

!!

!!

!Pane

l!D!

!!

!!

!!

!193516/68

0.0020

0.0023

0.0043

1.8490

0.0074

0.0074

0.0147

1.9990

193516/68

0.0016

0.0026

0.0041

1.6110

0.0053

0.0070

0.0123

1.7630

1935145

0.0025

0.0042

0.0067

1.5990

0.0083

0.0111

0.0194

1.7510

1935145

0.0009

0.0045

0.0054

1.2060

0.0036

0.0105

0.0141

1.3420

1946155

0.0014

0.0011

0.0025

2.3540

0.0078

0.0031

0.0109

3.5030

1946155

0.0006

0.0014

0.0020

1.4690

0.0052

0.0033

0.0085

2.5520

195616/68

0.0019

0.0017

0.0037

2.1260

0.0062

0.0075

0.0137

1.8210

195616/68

0.0029

0.0019

0.0048

2.5370

0.0071

0.0068

0.0140

2.0420

1935140

0.0035

0.0063

0.0098

1.5640

0.0132

0.0165

0.0297

1.7980

1935140

0.0013

0.0065

0.0078

1.1920

0.0060

0.0156

0.0216

1.3870

1941145

0.0014

0.0017

0.0031

1.8120

0.0027

0.0046

0.0073

1.5870

1941145

0.0006

0.0020

0.0026

1.2900

0.0008

0.0045

0.0053

1.1730

1946150

0.0018

0.0010

0.0028

2.8760

0.0079

0.0023

0.0102

4.4770

1946150

0.0012

0.0014

0.0026

1.8330

0.0058

0.0028

0.0086

3.0830

1951155

0.0011

0.0012

0.0023

1.9480

0.0078

0.0040

0.0118

2.9610

1951155

0.0001

0.0013

0.0015

1.0900

0.0046

0.0039

0.0085

2.1990

1956160

0.0007

0.0009

0.0017

1.8180

0.0046

0.0052

0.0097

1.8850

1956160

0.0006

0.0010

0.0016

1.6150

0.0044

0.0046

0.0090

1.9480

196116/68

0.0028

0.0023

0.0050

2.2140

0.0074

0.0091

0.0165

1.8120

196116/68

0.0043

0.0025

0.0068

2.7320

0.0090

0.0083

0.0173

2.0760

7/196812010

0.0036

0.0017

0.0053

3.1210

0.0151

0.0073

0.0223

3.0670

7/196812010

0.0056

0.0019

0.0075

3.8740

0.0171

0.0067

0.0238

3.5450

1970180

0.0085

0.0033

0.0118

3.5810

0.0272

0.0108

0.0379

3.5250

1970180

0.0131

0.0037

0.0168

4.4960

0.0329

0.0097

0.0426

4.3860

1980190

0.0066

0.0020

0.0086

4.2670

0.0237

0.0084

0.0321

3.8030

1980190

0.0114

0.0022

0.0136

6.2140

0.0335

0.0077

0.0412

5.3410

1990100

0.0015

0.0015

0.0030

2.0340

0.0124

0.0095

0.0219

2.3010

1990100

0.0029

0.0016

0.0045

2.7770

0.0091

0.0086

0.0178

2.0540

2000110

0.0009

0.0004

0.0013

2.9910

0.0094

0.0031

0.0124

4.0240

2000110

0.0007

0.0005

0.0012

2.4970

0.0092

0.0026

0.0118

4.5310

1970175

0.0064

0.0032

0.0096

3.0300

0.0203

0.0103

0.0306

2.9820

1970175

0.0089

0.0039

0.0129

3.2760

0.0192

0.0098

0.0290

2.9680

1975180

0.0111

0.0035

0.0146

4.1240

0.0346

0.0119

0.0465

3.9110

1975180

0.0180

0.0038

0.0218

5.7390

0.0459

0.0104

0.0563

5.3960

1980185

0.0089

0.0022

0.0112

4.9820

0.0285

0.0079

0.0364

4.5990

1980185

0.0129

0.0023

0.0152

6.6310

0.0357

0.0069

0.0427

6.1430

1985190

0.0037

0.0015

0.0052

3.3880

0.0163

0.0079

0.0242

3.0540

1985190

0.0087

0.0018

0.0106

5.7500

0.0271

0.0076

0.0347

4.5860

1990195

0.0016

0.0020

0.0036

1.8190

0.0124

0.0123

0.0247

2.0080

1990195

0.0041

0.0022

0.0063

2.8480

0.0079

0.0118

0.0197

1.6720

1995100

0.0014

0.0008

0.0022

2.6340

0.0106

0.0056

0.0162

2.9110

1995100

0.0015

0.0008

0.0023

2.7870

0.0096

0.0044

0.0140

3.1530

2000105

0.0009

0.0005

0.0014

2.6990

0.0098

0.0044

0.0142

3.2310

2000105

0.0006

0.0005

0.0011

2.1110

0.0090

0.0036

0.0126

3.5100

2005110

0.0008

0.0003

0.0011

3.5200

0.0076

0.0014

0.0091

6.3380

2005110

0.0009

0.0004

0.0012

3.2850

0.0082

0.0013

0.0095

7.1740

193512010

0.0029

0.0020

0.0048

2.4570

0.0117

0.0073

0.0190

2.5920

193512010

0.0038

0.0022

0.0060

2.7160

0.0119

0.0068

0.0187

2.7400

TABLE!5g:!V

alue


ortfolio!!!!!!!!!+!!!!!!!5x5!Dou

ble1Sort!Test!P

ortfolios!Bu

ilt!Using!Equ

al1W

eighted!Securitie

sCO

MPO

NEN

TS!OF!TH

E!VARIANCE

S!OF!TH

E

FF

FF

s2(�

0)

s2(�

0)

s2(�

0)

s2(�

1)

s2(�

1)

s2(�

1)

s2(�

0)

s2(�

0)

s2(�

0)

s2(�

1)

s2(�

1)

s2(�

1)

�j,

t

68

Period

! Pane

l!A!

!!

!!

!!

!Pane

l!C!

!!

!!

!!

!193516/68

11

11

11

11

193516/68

11

11

0.2136

0.0452

0.2589

5.7220

1935145

11

11

11

11

1935145

11

11

0.1589

0.0479

0.2068

4.3160

1946155

11

11

11

11

1946155

11

11

0.1225

0.0308

0.1533

4.9760

195616/68

11

11

11

11

195616/68

11

11

0.3221

0.0545

0.3766

6.9150

1935140

11

11

11

11

1935140

11

11

0.1916

0.0418

0.2334

5.5830

1941145

11

11

11

11

1941145

11

11

0.1193

0.0551

0.1745

3.1640

1946150

11

11

11

11

1946150

11

11

0.0829

0.0218

0.1047

4.8040

1951155

11

11

11

11

1951155

11

11

0.1612

0.0398

0.2010

5.0500

1956160

11

11

11

11

1956160

11

11

0.1771

0.0418

0.2190

5.2370

196116/68

11

11

11

11

196116/68

11

11

0.4156

0.0629

0.4785

7.6080

7/196812010

11

11

11

11

7/196812010

11

11

0.3451

0.0984

0.4434

4.5070

1970180

11

11

11

11

1970180

11

11

0.5767

0.1710

0.7477

4.3730

1980190

11

11

11

11

1980190

11

11

0.2798

0.1124

0.3923

3.4890

1990100

11

11

11

11

1990100

11

11

0.3408

0.0456

0.3864

8.4820

2000110

11

11

11

11

2000110

11

11

0.2506

0.0707

0.3213

4.5460

1970175

11

11

11

11

1970175

11

11

0.7823

0.2048

0.9871

4.8200

1975180

11

11

11

11

1975180

11

11

0.3403

0.1547

0.4949

3.2000

1980185

11

11

11

11

1980185

11

11

0.2610

0.1238

0.3849

3.1080

1985190

11

11

11

11

1985190

11

11

0.2637

0.0982

0.3619

3.6840

1990195

11

11

11

11

1990195

11

11

0.3335

0.0531

0.3866

7.2760

1995100

11

11

11

11

1995100

11

11

0.3013

0.0326

0.3339

10.2400

2000105

11

11

11

11

2000105

11

11

0.2991

0.0524

0.3515

6.7050

2005110

11

11

11

11

2005110

11

11

0.1988

0.0836

0.2824

3.3770

193512010

11

11

11

11

193512010

11

11

0.2871

0.0750

0.3621

4.8280

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!B!

!!

!!

!!

!Pane

l!D!

!!

!!

!!

!193516/68

0.0012

0.0012

0.0025

2.0020

11

11

193516/68

0.0004

0.0013

0.0018

1.3330

0.2236

0.0569

0.2805

4.9280

1935145

0.0015

0.0014

0.0029

2.0330

11

11

1935145

0.0001

0.0016

0.0017

1.0700

0.1630

0.0591

0.2221

3.7600

1946155

0.0009

0.0005

0.0014

2.8160

11

11

1946155

0.0003

0.0006

0.0009

1.5700

0.0999

0.0418

0.1418

3.3890

195616/68

0.0013

0.0017

0.0030

1.7760

11

11

195616/68

0.0008

0.0017

0.0025

1.4930

0.3621

0.0671

0.4292

6.3950

1935140

0.0019

0.0021

0.0040

1.8790

11

11

1935140

10.000

10.0023

0.0022

0.9551

0.2226

0.0532

0.2758

5.1890

1941145

0.0010

0.0006

0.0016

2.7870

11

11

1941145

0.0004

0.0007

0.0010

1.5710

0.0890

0.0661

0.1550

2.3460

1946150

0.0006

0.0003

0.0009

3.4030

11

11

1946150

0.0003

0.0004

0.0007

1.7700

0.0799

0.0368

0.1167

3.1680

1951155

0.0011

0.0007

0.0019

2.6030

11

11

1951155

0.0004

0.0008

0.0011

1.4770

0.1191

0.0468

0.1659

3.5430

1956160

0.0010

0.0014

0.0023

1.7010

11

11

1956160

0.0005

0.0013

0.0017

1.3560

0.1632

0.0457

0.2089

4.5680

196116/68

0.0015

0.0019

0.0034

1.8140

11

11

196116/68

0.0011

0.0019

0.0030

1.5660

0.4912

0.0814

0.5726

7.0360

7/196812010

0.0030

0.0017

0.0047

2.7650

11

11

7/196812010

0.0028

0.0019

0.0047

2.5100

0.3908

0.1194

0.5103

4.2720

1970180

0.0037

0.0018

0.0055

3.0320

11

11

1970180

0.0052

0.0021

0.0073

3.4340

0.6792

0.2227

0.9020

4.0490

1980190

0.0026

0.0019

0.0045

2.3990

11

11

1980190

0.0057

0.0021

0.0078

3.6450

0.4235

0.1326

0.5561

4.1950

1990100

0.0047

0.0029

0.0076

2.6470

11

11

1990100

0.0019

0.0030

0.0049

1.6230

0.3775

0.0577

0.4352

7.5470

2000110

0.0028

0.0010

0.0038

3.8950

11

11

2000110

0.0018

0.0008

0.0026

3.1090

0.2194

0.0659

0.2853

4.3270

1970175

0.0034

0.0017

0.0051

3.0040

11

11

1970175

0.0024

0.0021

0.0045

2.1140

0.7969

0.2736

1.0710

3.9120

1975180

0.0046

0.0021

0.0067

3.1650

11

11

1975180

0.0082

0.0024

0.0106

4.4070

0.5622

0.1977

0.7599

3.8430

1980185

0.0033

0.0015

0.0047

3.2280

11

11

1980185

0.0056

0.0016

0.0071

4.4790

0.3561

0.1387

0.4949

3.5670

1985190

0.0016

0.0021

0.0036

1.7610

11

11

1985190

0.0049

0.0024

0.0073

3.0130

0.4381

0.1219

0.5599

4.5950

1990195

0.0050

0.0037

0.0087

2.3510

11

11

1990195

0.0018

0.0041

0.0059

1.4250

0.4274

0.0715

0.4989

6.9810

1995100

0.0037

0.0017

0.0054

3.2400

11

11

1995100

0.0017

0.0015

0.0032

2.1840

0.2753

0.0374

0.3126

8.3680

2000105

0.0045

0.0015

0.0060

3.9340

11

11

2000105

0.0026

0.0013

0.0039

3.0090

0.2577

0.0506

0.3083

6.0880

2005110

0.0007

0.0003

0.0010

3.5230

11

11

2005110

0.0007

0.0003

0.0009

3.5950

0.1860

0.0767

0.2627

3.4240

193512010

0.0022

0.0015

0.0037

2.4850

11

11

193512010

0.0018

0.0016

0.0034

2.0870

0.3171

0.0919

0.4090

4.4500

FF

FF

TABLE!5g:!V

alue


ortfolio!!!!!!!!!+!!!!!!!5x5!Dou

ble1Sort!Test!P

ortfolios!Bu

ilt!Using!Equ

al1W

eighted!Securitie

sCO

MPO

NEN

TS!OF!TH

E!VARIANCE

S!OF!TH

E!!!!!!!!!!!!!(con

t.)

s2(�

2)

s2(�

2)

s2(�

2)

s2(�

3)

s2(�

3)

s2(�

3)

s2(�

2)

s2(�

2)

s2(�

2)

s2(�

3)

s2(�

3)

s2(�

3)

�j,

t

69

!!

!!

!!

!

Period

Period

!!

!!

!!

!!

!Pane

l!A!

!!

!!

!!

!Pane

l!C!

!!

!!

!!

!193516/68

0.0013

0.0011

0.0024

2.0960

0.0015

0.0007

0.0022

3.3370

193516/68

0.0013

0.0012

0.0025

2.0860

0.0015

0.0013

0.0027

2.1480

1935145

0.0023

0.0022

0.0044

2.0640

0.0023

0.0010

0.0032

3.3990

1935145

0.0023

0.0022

0.0045

2.0740

0.0024

0.0021

0.0044

2.1320

1946155

0.0007

0.0007

0.0014

2.1080

0.0012

0.0004

0.0016

3.9960

1946155

0.0008

0.0007

0.0015

2.2200

0.0013

0.0007

0.0020

2.8180

195616/68

0.0008

0.0006

0.0014

2.2260

0.0012

0.0006

0.0018

2.9320

195616/68

0.0008

0.0007

0.0015

2.0590

0.0008

0.0010

0.0018

1.8040

1935140

0.0038

0.0029

0.0067

2.2870

0.0030

0.0013

0.0043

3.2400

1935140

0.0039

0.0029

0.0069

2.3390

0.0039

0.0027

0.0066

2.4310

1941145

0.0006

0.0012

0.0018

1.4860

0.0015

0.0005

0.0020

3.9070

1941145

0.0005

0.0013

0.0018

1.4140

0.0006

0.0013

0.0019

1.4480

1946150

0.0012

0.0006

0.0018

2.9110

0.0015

0.0003

0.0018

6.0530

1946150

0.0011

0.0006

0.0017

2.8800

0.0019

0.0007

0.0026

3.7880

1951155

0.0002

0.0007

0.0009

1.3240

0.0008

0.0005

0.0013

2.7140

1951155

0.0005

0.0008

0.0013

1.6540

0.0008

0.0008

0.0015

1.9900

1956160

0.0002

0.0006

0.0007

1.2670

0.0004

0.0006

0.0010

1.6510

1956160

0.0001

0.0007

0.0009

1.1900

0.0005

0.0008

0.0012

1.5810

196116/68

0.0012

0.0007

0.0019

2.7410

0.0017

0.0006

0.0023

3.7000

196116/68

0.0012

0.0007

0.0020

2.6240

0.0010

0.0011

0.0022

1.9170

7/196812010

0.0007

0.0010

0.0017

1.7190

0.0019

0.0009

0.0028

3.2490

7/196812010

0.0010

0.0011

0.0020

1.9130

0.0012

0.0019

0.0031

1.6290

1970180

0.0015

0.0011

0.0026

2.2940

0.0028

0.0008

0.0036

4.4480

1970180

0.0018

0.0011

0.0029

2.6550

0.0011

0.0027

0.0037

1.4070

1980190

0.0007

0.0013

0.0020

1.4920

0.0020

0.0012

0.0032

2.6410

1980190

0.0007

0.0014

0.0022

1.5180

0.0014

0.0027

0.0041

1.5110

1990100

0.0002

0.0011

0.0013

1.2170

0.0014

0.0011

0.0026

2.3040

1990100

0.0007

0.0012

0.0018

1.5550

0.0011

0.0014

0.0025

1.8240

2000110

0.0003

0.0006

0.0009

1.4080

0.0015

0.0006

0.0021

3.5390

2000110

0.0005

0.0008

0.0013

1.6690

0.0013

0.0011

0.0025

2.1710

1970175

0.0020

0.0012

0.0032

2.6950

0.0031

0.0008

0.0039

4.8430

1970175

0.0024

0.0012

0.0036

2.9490

0.0013

0.0028

0.0041

1.4600

1975180

0.0008

0.0011

0.0020

1.7440

0.0025

0.0009

0.0034

3.9000

1975180

0.0013

0.0011

0.0024

2.1950

0.0003

0.0027

0.0030

1.0990

1980185

0.0010

0.0010

0.0020

1.9360

0.0021

0.0009

0.0029

3.3980

1980185

0.0011

0.0010

0.0021

2.0790

0.0019

0.0024

0.0043

1.7920

1985190

0.0003

0.0015

0.0018

1.2280

0.0017

0.0014

0.0031

2.2090

1985190

0.0003

0.0017

0.0020

1.2010

0.0009

0.0028

0.0037

1.3270

1990195

0.0001

0.0012

0.0013

1.0780

0.0011

0.0011

0.0023

2.0280

1990195

0.0003

0.0013

0.0016

1.2440

0.0008

0.0014

0.0022

1.5340

1995100

0.0005

0.0009

0.0014

1.5010

0.0017

0.0010

0.0027

2.6800

1995100

0.0011

0.0010

0.0021

2.0840

0.0014

0.0012

0.0026

2.1500

2000105

0.0001

0.0007

0.0007

1.0960

0.0010

0.0008

0.0018

2.3110

2000105

0.0004

0.0008

0.0013

1.5520

0.0006

0.0012

0.0018

1.5440

2005110

0.0004

0.0005

0.0009

1.7820

0.0019

0.0004

0.0023

6.1240

2005110

0.0005

0.0007

0.0012

1.7080

0.0019

0.0010

0.0029

3.0080

193512010

0.0009

0.0011

0.0020

1.8970

0.0018

0.0008

0.0025

3.2800

193512010

0.0011

0.0011

0.0022

1.9920

0.0013

0.0016

0.0029

1.8070

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!B!

!!

!!

!!

!Pane

l!D!

!!

!!

!!

!193516/68

10.000

20.0064

0.0061

0.9654

0.0033

0.0191

0.0225

1.1730

193516/68

10.000

70.0072

0.0065

0.8991

0.0022

0.0197

0.0219

1.1110

1935145

10.002

30.0101

0.0078

0.7749

10.001

60.0238

0.0223

0.9344

1935145

10.003

70.0110

0.0073

0.6640

10.002

80.0242

0.0214

0.8828

1946155

0.0002

0.0043

0.0046

1.0550

0.0047

0.0124

0.0171

1.3780

1946155

0.0005

0.0052

0.0058

1.1020

0.0049

0.0129

0.0178

1.3800

195616/68

0.0013

0.0047

0.0060

1.2680

0.0067

0.0205

0.0272

1.3260

195616/68

0.0009

0.0055

0.0064

1.1580

0.0046

0.0211

0.0257

1.2160

1935140

10.002

10.0133

0.0111

0.8408

0.0015

0.0297

0.0312

1.0500

1935140

10.004

70.0142

0.0095

0.6708

10.000

60.0299

0.0293

0.9793

1941145

10.002

40.0064

0.0040

0.6325

10.004

90.0169

0.0120

0.7101

1941145

10.002

40.0071

0.0047

0.6621

10.005

20.0176

0.0124

0.7044

1946150

0.0007

0.0037

0.0044

1.1970

0.0046

0.0083

0.0129

1.5570

1946150

0.0007

0.0044

0.0051

1.1570

0.0049

0.0087

0.0136

1.5610

1951155

10.000

20.0050

0.0048

0.9647

0.0050

0.0164

0.0214

1.3030

1951155

0.0003

0.0061

0.0063

1.0420

0.0052

0.0171

0.0223

1.3020

1956160

0.0003

0.0027

0.0030

1.0950

0.0081

0.0155

0.0236

1.5250

1956160

10.000

20.0031

0.0029

0.9467

0.0066

0.0154

0.0220

1.4250

196116/68

0.0020

0.0060

0.0080

1.3280

0.0060

0.0238

0.0298

1.2530

196116/68

0.0016

0.0071

0.0087

1.2230

0.0035

0.0249

0.0284

1.1400

7/196812010

0.0003

0.0063

0.0066

1.0410

0.0037

0.0263

0.0300

1.1390

7/196812010

0.0009

0.0069

0.0078

1.1240

0.0044

0.0265

0.0309

1.1660

1970180

0.0009

0.0117

0.0125

1.0760

0.0062

0.0368

0.0430

1.1700

1970180

0.0032

0.0126

0.0159

1.2560

0.0060

0.0368

0.0427

1.1620

1980190

0.0004

0.0079

0.0083

1.0560

0.0054

0.0329

0.0384

1.1660

1980190

0.0006

0.0089

0.0095

1.0660

0.0050

0.0339

0.0389

1.1480

1990100

10.000

40.0047

0.0042

0.9060

10.001

30.0315

0.0302

0.9575

1990100

10.000

30.0053

0.0050

0.9405

0.0008

0.0315

0.0323

1.0260

2000110

10.000

30.0015

0.0012

0.8033

0.0007

0.0106

0.0113

1.0700

2000110

10.000

40.0016

0.0012

0.7437

0.0041

0.0099

0.0140

1.4180

1970175

0.0002

0.0119

0.0121

1.0200

0.0008

0.0360

0.0368

1.0230

1970175

0.0002

0.0133

0.0135

1.0140

0.0009

0.0378

0.0387

1.0230

1975180

0.0039

0.0113

0.0152

1.3450

0.0157

0.0377

0.0534

1.4170

1975180

0.0078

0.0118

0.0196

1.6640

0.0162

0.0361

0.0523

1.4470

1980185

0.0012

0.0086

0.0098

1.1440

0.0097

0.0326

0.0423

1.2990

1980185

0.0020

0.0094

0.0115

1.2170

0.0086

0.0327

0.0413

1.2620

1985190

0.0001

0.0063

0.0064

1.0210

0.0018

0.0295

0.0313

1.0620

1985190

10.000

30.0074

0.0071

0.9591

0.0016

0.0311

0.0327

1.0520

1990195

10.000

30.0055

0.0052

0.9462

0.0001

0.0348

0.0350

1.0040

1990195

10.000

70.0062

0.0054

0.8848

10.000

40.0350

0.0346

0.9891

1995100

10.000

60.0033

0.0027

0.8092

10.003

90.0243

0.0204

0.8402

1995100

0.0004

0.0039

0.0043

1.1020

0.0015

0.0239

0.0254

1.0610

2000105

10.000

60.0018

0.0012

0.6792

10.002

50.0159

0.0134

0.8418

2000105

10.000

60.0018

0.0013

0.6962

0.0033

0.0146

0.0179

1.2300

2005110

0.0000

0.0010

0.0010

1.0370

0.0041

0.0038

0.0079

2.0880

2005110

10.000

20.0013

0.0010

0.8169

0.0045

0.0039

0.0084

2.1480

193512010

0.0000

0.0063

0.0064

1.0070

0.0035

0.0232

0.0267

1.1510

193512010

0.0002

0.0071

0.0072

1.0220

0.0034

0.0235

0.0269

1.1450

TABLE!5h

:!Value


ortfolio!!!!!!!!!+!!!!!!!5x5!Dou

ble1Sort!Test!P

ortfolios!Bu

ilt!Using!Value

1Weighted!Securitie

sCO

MPO

NEN

TS!OF!TH

E!VARIANCE

S!OF!TH

E

FF

FF

s2(�

0)

s2(�

0)

s2(�

0)

s2(�

1)

s2(�

1)

s2(�

1)

s2(�

0)

s2(�

0)

s2(�

0)

s2(�

1)

s2(�

1)

s2(�

1)

�j,

t

70

Period

! Pane

l!A!

!!

!!

!!

!Pane

l!C!

!!

!!

!!

!193516/68

11

11

11

11

193516/68

11

11

0.1186

0.1789

0.2975

1.6630

1935145

11

11

11

11

1935145

11

11

0.0070

0.1644

0.1714

1.0430

1946155

11

11

11

11

1946155

11

11

0.1395

0.1474

0.2869

1.9460

195616/68

11

11

11

11

195616/68

11

11

0.1993

0.2167

0.4160

1.9200

1935140

11

11

11

11

1935140

11

11

0.0402

0.1325

0.1727

1.3030

1941145

11

11

11

11

1941145

11

11

10.035

60.2020

0.1665

0.8240

1946150

11

11

11

11

1946150

11

11

0.1659

0.0989

0.2647

2.6770

1951155

11

11

11

11

1951155

11

11

0.1120

0.1959

0.3079

1.5720

1956160

11

11

11

11

1956160

11

11

0.1510

0.2057

0.3567

1.7340

196116/68

11

11

11

11

196116/68

11

11

0.2322

0.2240

0.4562

2.0360

7/196812010

11

11

11

11

7/196812010

11

11

0.2623

0.3056

0.5679

1.8580

1970180

11

11

11

11

1970180

11

11

0.5721

0.5118

1.0840

2.1180

1980190

11

11

11

11

1980190

11

11

0.1535

0.3608

0.5143

1.4250

1990100

11

11

11

11

1990100

11

11

0.2076

0.1313

0.3389

2.5820

2000110

11

11

11

11

2000110

11

11

0.1979

0.2223

0.4202

1.8900

1970175

11

11

11

11

1970175

11

11

0.3630

0.6495

1.0120

1.5590

1975180

11

11

11

11

1975180

11

11

0.6099

0.4492

1.0590

2.3580

1980185

11

11

11

11

1980185

11

11

0.2282

0.2959

0.5241

1.7710

1985190

11

11

11

11

1985190

11

11

0.0681

0.4100

0.4781

1.1660

1990195

11

11

11

11

1990195

11

11

0.1615

0.1360

0.2975

2.1880

1995100

11

11

11

11

1995100

11

11

0.2430

0.1128

0.3558

3.1550

2000105

11

11

11

11

2000105

11

11

0.2928

0.1765

0.4693

2.6600

2005110

11

11

11

11

2005110

11

11

0.0876

0.2515

0.3391

1.3480

193512010

11

11

11

11

193512010

11

11

0.1986

0.2498

0.4485

1.7950

!!

!!

!!

!!

!!

!!

!!

!!

!!

Pane

l!B!

!!

!!

!!

!Pane

l!D!

!!

!!

!!

!193516/68

0.0005

0.0033

0.0038

1.1460

11

11

193516/68

0.0003

0.0036

0.0039

1.0810

0.1202

0.2056

0.3258

1.5850

1935145

10.000

40.0029

0.0025

0.8692

11

11

1935145

10.000

40.0032

0.0028

0.8751

0.0143

0.1898

0.2042

1.0750

1946155

0.0006

0.0019

0.0026

1.3230

11

11

1946155

0.0007

0.0022

0.0029

1.2910

0.1409

0.1814

0.3223

1.7770

195616/68

0.0012

0.0047

0.0059

1.2440

11

11

195616/68

0.0007

0.0052

0.0058

1.1270

0.1963

0.2387

0.4350

1.8220

1935140

10.000

40.0035

0.0030

0.8746

11

11

1935140

10.000

50.0039

0.0034

0.8703

0.0472

0.1629

0.2101

1.2900

1941145

10.000

30.0021

0.0019

0.8774

11

11

1941145

10.000

20.0023

0.0021

0.9006

10.029

30.2217

0.1924

0.8679

1946150

0.0003

0.0010

0.0012

1.2660

11

11

1946150

0.0003

0.0012

0.0015

1.2330

0.1661

0.1364

0.3024

2.2180

1951155

0.0010

0.0029

0.0039

1.3530

11

11

1951155

0.0011

0.0033

0.0043

1.3230

0.1101

0.2265

0.3366

1.4860

1956160

0.0021

0.0043

0.0064

1.5010

11

11

1956160

0.0016

0.0044

0.0059

1.3580

0.1269

0.2112

0.3381

1.6010

196116/68

0.0006

0.0050

0.0056

1.1110

11

11

196116/68

0.0001

0.0057

0.0058

1.0200

0.2436

0.2571

0.5007

1.9480

7/196812010

0.0003

0.0062

0.0065

1.0520

11

11

7/196812010

0.0005

0.0065

0.0070

1.0710

0.2723

0.3360

0.6083

1.8100

1970180

0.0008

0.0061

0.0069

1.1230

11

11

1970180

0.0013

0.0067

0.0080

1.2010

0.6343

0.5713

1.2060

2.1100

1980190

0.0005

0.0075

0.0081

1.0720

11

11

1980190

0.0002

0.0084

0.0086

1.0260

0.1806

0.4002

0.5808

1.4510

1990100

10.000

50.0101

0.0096

0.9513

11

11

1990100

10.000

90.0104

0.0096

0.9174

0.2195

0.1499

0.3694

2.4640

2000110

10.000

60.0037

0.0030

0.8289

11

11

2000110

0.0001

0.0033

0.0034

1.0420

0.1637

0.2331

0.3968

1.7020

1970175

0.0002

0.0057

0.0059

1.0390

11

11

1970175

0.0002

0.0064

0.0066

1.0290

0.3394

0.7240

1.0630

1.4690

1975180

0.0025

0.0067

0.0091

1.3730

11

11

1975180

0.0034

0.0070

0.0104

1.4850

0.6997

0.4801

1.1800

2.4570

1980185

0.0019

0.0066

0.0085

1.2830

11

11

1980185

0.0014

0.0072

0.0086

1.1950

0.2857

0.3240

0.6098

1.8820

1985190

10.000

60.0075

0.0070

0.9249

11

11

1985190

10.000

70.0085

0.0078

0.9174

0.0731

0.4534

0.5265

1.1610

1990195

0.0002

0.0107

0.0109

1.0190

11

11

1990195

10.000

80.0112

0.0104

0.9303

0.1557

0.1485

0.3041

2.0480

1995100

10.001

50.0082

0.0067

0.8151

11

11

1995100

10.001

00.0083

0.0072

0.8766

0.2788

0.1357

0.4145

3.0540

2000105

10.001

40.0061

0.0047

0.7737

11

11

2000105

0.0002

0.0053

0.0055

1.0350

0.3098

0.1799

0.4897

2.7220

2005110

0.0002

0.0007

0.0010

1.3090

11

11

2005110

0.0001

0.0008

0.0009

1.1120

0.0114

0.2689

0.2803

1.0420

193512010

0.0004

0.0049

0.0053

1.0790

11

11

193512010

0.0004

0.0053

0.0056

1.0730

0.2050

0.2786

0.4836

1.7360

FF

FF

TABLE!5h

:!Value


ortfolio!!!!!!!!!+!!!!!!!5x5!Dou

ble1Sort!Test!P

ortfolios!Bu

ilt!Using!Value

1Weighted!Securitie

sCO

MPO

NEN

TS!OF!TH

E!VARIANCE

S!OF!TH

E!!!!!!!!!!!!!(con

t.)

s2(�

2)

s2(�

2)

s2(�

2)

s2(�

3)

s2(�

3)

s2(�

3)

s2(�

2)

s2(�

2)

s2(�

2)

s2(�

3)

s2(�

3)

s2(�

3)

�j,

t

71

Documents

Fama-MacBeth 1973: Replication and Extension - SP …home.uchicago.edu/~serginio/research/FamaPaper_fm73... · · 2013-10-12Fama-MacBeth 1973: Replication and Extension ... alternate